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All Textbook Solutions for College Physics
Identify the type of energy transferred to your body in each of the following as either internal energy, heat transfer, or doing work: (a) basking in sunlight (b) eating food; (c) riding an elevator to a higher floor.A great deal of effort time, and money has been spent in the quest for the so-called perpetual-motion machine, which is defined as a hypothetical machine that operates or produces useful work indefinitely and/or a hypothetical machine that produces more work or energy than it consumes. Explain, in terms of heat engines and the first law of thermodynamics, why or why not such a machine is likely to be constructed.One method of converting heat transfer to doing work is for heat transfer into a gas to take place, which expands, dong work on a piston, as shown in the figure below. (a) Is the heat transfer converted directly to work in an isobaric process, or does it go through another form first? Explain your answer. (b) What about in an isothermal process? (c) What about in an adiabatic process (where heat transfer occurred prior to the adiabatic process)?Would the previous question make any sense for an isochoric process? Explain your answer.We ordinarily say that U=0 for an isothermal process. Does this assume no phase change takes place? Explain your answer.The temperature of a rapidly expanding gas decreases. Explain why in terms of the first law of thermodynamics. (Hint: Consider whether the gas does work and whether heat transfer occurs rapidly into the gas through conduction.)Which cyclical process represented by the two closed loops, ABCFA end ABDEA, on the PV diagram in the figure below produces the greatest net work? Is that process else the one with the smallest work input required to return it to point A? Explain your responses. Figure 15.42 The two cyclical processes shown on this PV diagram start with and return the system to the conditions at point A, but they follow different paths and produce different amounts of work.A real process may be nearly adiabatic if it occurs over a very short time. How does the short time span help the process to be adiabatic?It is unlikely that a process can be isothermal unless it is a very slow process. Explain why. Is the same true for isobaric and isochoric processes? Explain your answer.Imagine you are driving a car up Pike’s Peak in Colorado. To raise a car weighing 1000 kilograms a distance of 100 meters would require about a million joules. You could raise a car 12.5 kilometers with the energy in a gallon of gas. Driving up Pike’s Peak (a mere 3000-meter climb) should consume a little less than a quart of gas. But other considerations have to be taken into account. Explain, in terms of efficiency, what factors may keep you from realizing your ideal energy use on this trip.Is a temperature difference necessary to operate a heal engine? State why or why not.Definitions of efficiency vary depending on how energy is being converted. Compare the definitions of efficiency for the human body and heat engines. How does the definition of eficiency in each relate to the type of energy being converted into doing walk?Whyother than the fact that the second law of thermodynamics says reversible engines are the most ef?cientShould heat engines employing reversible processes be more ef?cient than those employing irreversible processes? Consider that dissipative mechanisms are one cause of irreversibility.Think about the drinking bird at the beginning of this section (Figure 15.21). Although the bird enjoys the theoretical maximum efficiency possible, it left to its own devices ever time, the bird will cease “drinking." What are some of the dissipative processes that might cause the bird's motion to cease? Figure 15.21 This novelty toy, known as the drinking bird, IS an example of Carnot's engine. It contains methylene chloride (mixed with a dye) in the abdomen, which boils at a very low temperature—about 100°F. To operate, one gets the bird's head wet. As the water evaporates, fluid moves up into the head, causing the bird to become top-heavy and dip forward back into the water. This cools down the methylene chloride in the head, and it moves back into the abdomen, causing the bird to become bottom heavy and tip up. Except for a very small Input of energy—the original head- wetting—the bird becomes a perpetual motion machine of sorts. (credit: Arabesk.nl, Wikimedia Commons)Can improved engineering and materials be employed in heat engines to reduce heat transfer into the environment? Can they eliminate heat transfer into the environment entirely?Does the second law of thermodynamics alter the conservation of energy principle?Explain why heat pumps do not work as well in very cold climates as they do in milder ones. Is the same true of refrigerators?In some Northern European nations, homes are being built without heating systems of any type. They are very well insulated and are kept warm by the body heal of the residents. However, when the residents are not at home, it is still warm in these houses. What is a possible explanation?Why do refrigerators, air conditioners, and heat pumps operate most costeffectively for cycles with a small difference between Th and Tc? (Note that the temperatures of the cycle employed are crucial to its COP.)Grocery store managers contend that there is less total energy consumption in the summer it the store is kept at a low temperature. Make arguments to support or refute this claim, taking into account that there are numerous refrigerators and freezers in the store.Can you cool a kitchen by leaving the refrigerator door open?A woman shuts her summer cottage up in September and returns in June. No one has entered the cottage in the meantime. Explain what she is likely to find, in terms of the second law of thermodynamics.Consider a system with a certain energy content, from which we wish to extract as much work as possible. Should the system's entropy be high or low? IS this orderly or disorderly? Structured or uniform? Explain briefly.Does a gas become more orderly when it liquefies? Does its entropy change? If s, does the entropy increase or decrease? Explain your answer.Explain how water’s entropy can decrease when it freezes without violating the second law of thermodynamics. Specifically, explain what happens to the entropy of its surroundings.Is a uniform-temperature gas more or less orderly than one with several different temperatures? Which is more structured? In which can heat transfer result in work done without heat transfer from another system?Give an example of a spontaneous process in which a system becomes less ordered and energy becomes less available to do work. What happens to the system's entropy in this process?What is the change in entropy in an adiabatic process? Does this imply that adiabatic processes are reversible? Can a process be precisely adiabatic for a macroscopic system?Does the entropy at a star increase or decrease as it radiates? Does the entropy of the space into which it radiates (which has a temperature of about 3 K) increase or decrease? What does this do to the entropy of the universe?Explain why a building made of bricks has smaller entropy than the same bricks in a disorganized pile. Do this by considering the number of ways that each could be formed (the number of microstates in each macrostate).Explain why a building made of bricks has smaller entropy than the same bricks in a disorganized pile. Do this by considering the number of ways that each could be formed (the number of microstates in each macrostate).What is the change in internal energy of a car if you put 12.0 gal of gasoline into its tank? The energy content of gasoline is 1.3108J/gal. All other factors, such as the car‘s temperature, are constant.How much heat transfer occurs from a system, if its internal energy decreased by 150 J while it was doing 30.0 J of work?A system does 1.80108J of work while 7.50108J of heat transfer occurs to the environment. What is the change in internal energy of the system assuming no other changes (such as in temperature or by the addition of fuel)?What is the change in internal energy of a system which does 4.50105J of work while 3.00106J of heat transfer occurs into the system, and 8.00106J of heat transfer occurs to the environment?Suppose a woman does 500 J of work and 9500 J of heat transfer occurs into the environment in the process. (a) What is the decrease in her internal energy, assuming no change in temperature or consumption of feed? (That is, there is no other energy transfer.) (b) What is her eficiency?(a) How much food energy will a man metabolize in the process of doing 35.0 kJ of work with an efficiency of 5.00%? (b) How much heal transfer occurs to the environment to keep his temperature constant? Explicitly show how you follow the steps in the Problem—Solving Strategy for thermodynamics found in Problem-Solving Strategies for Thermodynamics.(a) What is the average metabolic rate in watts of a man who metabolizes 10,500 kJ of feed energy in one day? (b) What is the maximum amount of work in joules he can do without breaking down fat, assuming a maximum eficiency of 20.0%? (c) Compare his work output with the daily output of a 187W (0.250horsepower) motor.(a) How long will the energy in a 1470kJ (350kcal) cup of yogurt last in a woman doing work at the rate of 150 W with an efficiency of 20.0% (such as in leisurely climbing stairs)? (b) Does the time found in part (a) imply that it is easy to consume more food energy than you can reasonably expect to work off with exercise?(a) A woman climbing the Washington Monument metabolizes 6.00102kJ of food energy. If her efficiency is 18.0%, how much heat transfer occurs to the environment to keep her temperature constant? (b) Discuss the amount of heat transfer found in (a). Is it consistent with the fact that you quickly warm up when exercising?A car tire contains 0.0380m3 S of air at a pressure of 2.20105N/m2 (about 32 psi). How much more internal energy does this gas have than the same volume has at zero gauge pressure (which is equivalent to normal atmospheric pressure)?A heliumfilled toy balloon has a gauge pressure of 0.200 atm and a volume of 10.0 L. How much greater is the internal energy of the helium in the balloon than it would be at zero gauge pressure?Steam to drive an old—fashioned steam locomotive is supplied at a constant gauge pressure of 1.75106N/m2 (about 250 psi) to a piston with a 0.200m radius. (a) By calculating PV, find the work done by the steam when the piston moves 0.800 m. Note that this is the net work output, since gauge pressure is used. (b) Now find the amount of work by calculating the force exerted times the distance traveled. Is the answer the same as in part (a)?A hand—driven tire pump has a piston with a 2.50cm diameter and a maximum stroke of 30.0 cm. (a) How much work do you do in one stroke if the average gauge pressure is 2.40105N/m2 (about 35 psi)? (b) What average force do you exert on the piston, neglecting friction and gravitational force?Calculate the net work output of a heat engine following path ABCDA in the figure below.What is the net work output of a heat engine that follows path ABBA in the figure above, with a straight line from B to D? Why is the work output less than for path ABCDA? Explicitly show how you follow the steps in the Problem Solving Strategies for Thermodynamics.Unreasonable Results What is wrong with the claim that a cyclical heat engine does 4.00 kJ of work on an input of 24.0 kJ of heal transfer while 16.0 kJ of heat transfers to the environment?(a) A cyclical heat engine, operating between temperatures of 450C and 150C produces 4.00 MJ of work on a heat transfer of 5.00 MJ into the engine. How much heat transfer occurs to the environment? (b) What is unreasonable about the engine? (c) Which premise is unreasonable?Construct Your Own Problem Consider a car's gasoline engine. Construct a problem in which you calculate the maximum efficiency this engine can have. Among the things to consider are the effective hot and cold reservoir temperatures. Compare your calculated eficiency with the actual efficiency of car engines.Construct Your Own Problem Consider a car trip into the mountains. Construct a problem in which you calculate the overall efficiency of the car for the trip as a ratio of kinetic and potential energy gained to fuel consumed. Compare this efficiency to the thermodynamic efficiency quoted for gasoline engines and discuss why the thermodynamic eficiency is so much greater. Among the factors to he considered are the gain in altitude and speed, the mass of the car, the distance traveled, and typical fuel economy.A certain heat engine does 10.0 kJ of work and 8.50 kJ of heat transfer occurs to the environment in a cyclical process. (a) What was the heal transfer into this engine? (b) What was the engine‘s efficiency?With 2.56106J of heat transfer into this engine, a given cyclical heat engine can do only 1.50105J of work. (a) What is the engine's efficiency? (b) How much heat transfer to the environment takes place?(a) What is the work output of a cyclical heat engine having a 22.0% eficiency and 6.00109J of heat transfer into the engine? (b) How much heat transfer occurs to the environment?(a) What is the eficiency of a cyclical heat engine in which 75.0 kJ of heat transfer occurs to the environment for every 95.0 kJ of heat transfer into the engine? (b) How much work does it produce for 100 kJ of heat transfer into the engine?The engine of a large Ship does 2.00108J of work with an eficiency of 5.00%. (a) How much heat transfer occurs to the environment? (b) How many barrels of fuel are consumed, if each barrel produces 6.00109J of heat transfer when burned?(a) How much heat transfer occurs to the environment by an electrical power station that uses 1.251014J of heat transfer into the engine with an efficiency of 42.0%? (b) What is the ratio of heat transfer to the environment to work output? (c) How much work is done?Assume that the turbines at a coal—powered power plant were upgraded, resulting in an improvement in eficiency of 3.32%. Assume that prior to the upgrade the power station had an eficiency of 36% and that the heat transfer into the engine in one day is still the same at 2.501014J. (a) How much more electrical energy is produced due to the upgrade? (b) How much less heat transfer occurs to the environment due to the upgrade?This problem compares the energy output and heat transfer to the environment by two different types of nuclear power stationsone with the normal efficiency of 34.0%, and another with an improved efficiency of 40.0%. Suppose both have the same heat transfer into the engine in one day. 2.501014J. (a) How much more electrical energy is produced by the more efficient power station? (b) How much less heat transfer occurs to the environment by the more efficient power station? (One type of more ef?cient nuclear power station, the gas—cooled reactor, has not been reliable enough to be economically feasible in spite of its greater eficiency.)A certain gasoline engine has an efficiency of 30.0%. What would the hot reservoir temperature be for a Carnot engine having that eficiency, if it operates with a cold reservoir temperature of 200°C?A gascooled nuclear reactor operates between hot and cold reservoir temperatures of 700C and 27.0C. (a) What is the maximum eficiency of a heat engine operating between these temperatures? (b) Find the ratio of this eficiency to the Carnot eficiency of a standard nuclear reactor (found in Example 15.4).(a) What is the hot reservoir temperature of a Carnot engine that has an eficiency of 42.0% and a cold reservoir temperature of 210C ? (b) What must the hot reservoir temperature be for a real heat engine that achieves 0.700 of the maximum eficiency, but still has an efficiency of 42.0% (and a cold reservoir at 27.0C )? (c) Does your answer imply practical limits to the efficiency of car gasoline engines?Steam locomotives have an efficiency of 17.0% and operate with a hot steam temperature of 425C. (a) What would the cold reservoir temperature be if this were a Carnot engine? (b) What would the maximum eficiency of this steam engine be if its cold reservoir temperature were 150C ?Practical steam engines utilize 450C steam, which is later exhausted at 270C. (a) What is the maximum eficiency that such a heat engine can have? (b) Since 270C steam is still quite hot, at second steam engine is sometimes operated using the exhaust of the first. What is the maximum eficiency of the second engine if its exhaust has a temperature of 150C ? (c) What is the overall eficiency of the two engines? (d) Show that this is the same eficiency as a single Carnot engine operating between 450C and 150C. Explicitly show how you follow the steps in the Problem-Solving Strategies for Thermodynamics.A coalfired electrical power station has an efficiency of 38%. The temperature of the steam leaving the boiler is 550°C. What percentage of the maximum efficiency does this station obtain? (Assume the temperature of the environment is 20C .)Would you be willing to financially back an inventor who is marketing a device that she claims has 25 kJ of heat transfer at 600 K, has heat transfer to the environment at 300 K, and does 12 kJ of work? Explain your answer.Unreasonable Results (a) Suppose you want to design a steam engine that has heat transfer to the environment at 270C and has a Carnot eficiency of 0.800. What temperature of hot Steam must you use? (b) What is unreasonable about the temperature? (c) Which premise is unreasonable?Unreasonable Results Calculate the cold reservoir temperature of a steam engine that uses hot steam at 450°C and has a Carnot efficiency of 0.700. (b) What is unreasonable about the temperature? (c) Which premise is unreasonable?What is the coefficient of performance of an ideal heat pump that has heat transfer from a cold temperature of 5.0C to a hot temperature of 40.0C ?Suppose you have an ideal refrigerator that cools an environment at 20.0C and has heat transfer to another environment at 50.0C. What is its coefficient of performance?What is the best coefficient of performance possible for a hypothetical refrigerator that could make liquid nitrogen at 200C and has heal transfer to the environment at 35.0C ?In a very mild winter climate, a heat pump has heat transfer from an environment at 5.00C to one at 35.0C. What is the best possible coefficient of performance for these temperatures? Explicitly show how you follow the steps in the Problem-Solving Strategies for Thermodynamics.(a) What is the best coefficient of performance for a heat pump that has a hot reservoir temperature of 50.0C and a cold reservoir temperature of 20.0C ? (b) How much heat transfer occurs into the warm environment if 3.60107J of work (10.0kWh) is put into it? (c) If the cost of this work input is 10.0cent/kWh, haw does its cost compare with the direct heat transfer achieved by burning natural gas at a cost of 85.0 cents per therm. (A therm is a common unit of energy for natural gas and equals 1.055108J .)(a) What is the best coefficient of performance for a refrigerator that cools an environment at 30.0C and has heat transfer to another environment at 45.0C ? (b) How much work in joules must be done for a heat transfer of 4186 kJ from the cold environment? (c) What is the cost of doing this if the work costs 10.0 cents per 3.60106J (a kilowatthour)? (d) How many kJ of heat transfer occurs into the warm environment? (e) Discuss what type of refrigerator might operate between these temperatures.Suppose you want to operate an ideal refrigerator with a cold temperature of 10.0C, and you would like it to have a coefficient of performance 7.00. What is the hot reservoir temperature for such a refrigerator?An ideal heat pump is being considered for use in heating an environment with a temperature of 22.0C. What is the cold reservoir temperature if the pump is to have a coefficient of performance of 12.0 ?A 4ton air conditioner removes 5.60107J (48,000 British thermal units) from a cold environment in 1.00 h. (a) What energy input in joules is necessary to do this if the air conditioner has an energy efficiency rating (EER) of 12.0? (b) What is the cost of doing this if the work costs 10.0 cents per 3.60106J (one kilowatt—hour)? (c) Discuss whether this cost seems realistic. Note that the energy efficiency rating (EER) of an air conditioner or refrigerator is defined to be the number of British thermal units of heat transfer from a cold environment per hour divided by the watts of power input.Show that the coefficients of performance of refrigerators and heat pumps are related by COPref=COPhp1. Start with the definitions of the COP s and the conservation of energy relationship between Qh, QC, and W.(a) On a winter day, a certain house loses 5.00108J of heat to the outside (about 500,000 Btu). What is the total change in entropy due to this heat transfer alone, assuming an average indoor temperature of 21.0C and an average outdoor temperature of 5.00C ? (b) This large change in entropy implies a large amount of energy has become unavailable to do work. Where do we find more energy when such energy is lost to us?On a hot summer day, 4.00106J of heat transfer into a parked car takes place, increasing its temperature from 35.0C to 45.0C. What is the increase in entropy of the car due to this heat transfer alone?A hot rock ejected from a volcano's lava fountain cools from 1100C to 40.0C, and its entropy decreases by 950J/K. How much heat transfer occurs from the rock?When 1.60105J of heat transfer occurs into a meat pie initially at 20.0C, its entropy increases by 480J/K. What is its final temperature?The Sun radiates energy at the rate of 3.801026W from its 5500C surface into dark empty space (a negligible fraction radiates onto Earth and the other planets). The effective temperature of deep space is 270C. (a) What is the increase in entropy in one day due to this heat transfer? (b) How much work is made unavailable?(a) In reaching equilibrium, how much heat transfer occurs from 1.00 kg of water at 40.0C when it is placed in contact with 1.00 kg of 20.0C water in reaching equilibrium? (b) What is the change in entropy due to this heat transfer? (c) How much work is made unavailable, taking the lowest temperature to be 20.0C ? Explicitly show how you follow the steps in the Problem-Solving Strategies for Entropy.What is the decrease in entropy of 25.0 g of water that condenses on a bathroom mirror at a temperature of 35.0C, assuming no change in temperature and given the latent heal of vaporization to be 2450kJ/kg ?Find the increase in entropy of 1.00 kg of liquid nitrogen that starts at its boiling temperature, boils, and warms to 20.0C at constant pressure.A large electrical power station generates 1000 MW of electricity with an efficiency of 35.0%. (a) Calculate the heat transfer to the power station, Qh, in one day. (b) How much heat transfer Qc occurs to the environment in one day? (c) If the heat transfer in the cooling towers is from 35.0C water into the local air mass, which increases in temperature from 18.0C to 20.0C, what is the total increase in entropy due to this heat transfer? (d) How much energy becomes unavailable to do work because of this increase in entropy, assuming an 18.0C lowest temperature? (Part of Qccould be utilized to operate heat engines or far simply heating the surroundings, but it rarely is.)(a) How much heat transfer occurs from 20.0 kg of 90.0C water placed in contact with 20.0 kg of 10.0C water, producing a final temperature of 50.0C ? (b) How much work could a Carnot engine do with this heat transfer, assuming it operates between two reservoirs at constant temperatures of 90.0C and 10.0C ? (c) What increase in entropy is produced by mixing 20.0 kg of 90.0C water with 20.0 kg of 10.0C water? (d) Calculate the amount of work made unavailable by this mixing using a low temperature of 10.0C, and compare it with the work done by the Garnet engine. Explicitly show how you follow the steps in the Problem-Solving Strategies for Entropy. (e) Discuss how everyday processes make increasingly more energy unavailable to do work, as implied by this problem.Using Table 15.4, verify the contention that if you toss 100 coins each second, you can expect to get 100 heads or 100 tails once in 21022 years; calculate the time to twodigit accuracy.What percent of the time will you get something in the range from 60 heads and 40 tails through 40 heads and 60 tails when tossing 100 coins? The total number of microstates in that range is 1.221030 . (Consult Table 15.4.)(a) If tossing 100 coins, how many ways (microstates) are there to get me three most likely macro states of 49 heads and 51 tails, 50 heads and 50 tails, and 51 heads and 49 tails? (b) What percent of the total possibilities is this? (Consult Table 15.4.)(a) What is the change in entropy if you start with 100 coins in the 45 heads and 55 tails macrostate, toss them, and get 51 heads and 49 tails? (b) What if you get 75 heads and 25 tails? (c) How much more likely is 51 heads and 49 tails than 75 heads and 25 tails? (d) Dues either outcome violate the second law of thermodynamics?(a) What is the change in entropy if you start with 10 coins in the 5 heads and 5 tails macrostate, toss them, and get 2 heads and 8 tails? (b) How much more likely is 5 heads and 5 tails than 2 heads and 8 tails? (Take the ratio of the number of microstates to find out.) (c) If you were betting on 2 heads and 8 tails would you accept odds of 252 to 45? Explain Why or why not. Table 15.5 10Coin Toss MacrostateNumber of Microstates (W) Heads Tails 10 0 1 9 1 10 8 2 45 7 3 120 6 4 210 5 5 252 4 6 210 3 7 120 2 8 45 1 9 10 0 10 1 Total: 1024(a) If you toss 10 coins, what percent of the time will you get the three most likely macrostates (6 heads and 4 tails, 5 heads and 5 tails, 4 heads and 6 tails)? (b) You can realistically toss 10 coins and count the number of heads and tails about twice a minute. At mat rate, how long will it take on average to get either 10 heads and 0 tails or 0 heads and 10 tails?(a) Construct a table showing the macro states and all of the individual microstates for tossing 13 coins. (Use Table 15.5 as a guide.) (b) How many macro states are there? (c) What is the total number of microstates? (d) What percent chance is here of tossing 5 heads and 1 tail? (e) How much more likely are you to toss 3 heads and 3 tails than 5 heads and 1 tail? (Take me ratio of the number of microstates to find out.)In an air conditioner, 12.65 MJ of heat transfer occurs from a cold environment in 1.00 h. (a) What mass of ice melting would involve the same heat transfer? (b) How many hours of operation would be equivalent to mailing 900 kg of ice? (c) If ice costs 20 cents per kg, do you think the air conditioner could be operated more cheaply than by simply using ice? Describe in detail how you evaluate the relative costs.Describe a system in which elastic potential energy is stored.What conditions must be met to produce simple harmonic motion?(a) If frequency is not constant for some oscillation, can the oscillation be simple harmonic motion? (b) Can you mink of any examples of harmonic motion where the frequency may depend on the amplitude?Give an example of a simple harmonic oscillator, specifically noting how its frequency is independent of amplitude.Explain why you expect an object made of a stiff material to vibrate at a higher frequency than a similar object made of a spongy material.As you pass freight truck with a trailer on a highway, you notice mat its trailer is bouncing up and down slowly. Is it more likely that the trailer is heavily loaded or nearly empty? Explain your answer.Some people modify cars to be much closet to me ground man when manufactured. Should they install stiffer springs? Explain your answer.Pendulum clocks are made to run at the correct rate by adjusting the pendulum's length. Suppose you move from one city to another where the acceleration due to gravity is slightly greater, taking your pendulum clock with you, will you have to lengthen or shorten the pendulum to keep the correct time, other factors remaining constant? Explain your answer.Explain in terms of energy how dissipative forces such as friction reduce the amplitude of a harmonic oscillator. Also explain how a driving mechanism can compensate. (A pendulum clock is such a system.)Give an example of a damped harmonic oscillator. (They we more common than undamped or simple harmonic oscillators.)How would a car bounce after a bump under each of these conditions? • overdamping • underdamping • critical dampingMost harmonic oscillators are damped and, if undriven, eventually come to a stop. How is this observation related to the second law of thermodynamics?Why are soldiers in general ordered to “route step" (walk out of step) across a bridge?Give one example of a transverse wave and another of a longitudinal wave, being careful to note the relative directions of the disturbance and wave propagation in each.What is the difference between propagation speed and the frequency of a wave? Does one or both affect wavelength? If so, how?Speakers in stereo systems have two colorcoded terminals to indicate how to hook up the wires. If the wires are reversed, the speaker moves in a direction opposite mat of a properly connected speaker. Explain why it is important to have both speakers connected the same way.Two identical waves undergo pure constructive interference. Is the resultant intensity twice that of the individual waves? Explain your answer.Circular water waves decrease in amplitude as they move away from where a rock is dropped. Explain why.Fish ate hung on a spring scale to determine their mass (most fishermen feel no obligation to truthfully report the mass). (a) What is the force constant at the spring in such a scale if it the spring stretches 8.00 cm for a 10.0 kg load? (b) What is the mass of a fish that stretches the spring 5.50 cm? (c) How far apart are the halfkilogram marks on the scale?It is weighin time for the local under85kg rugby team. The bathroom scale used to assess eligibility can be described by Hooke’s law and is depressed 0.75 cm by its maximum load of 120 kg. (a) What is me spring's effective spring constant? (b) A player stands on the scales and depresses it by 0.48 cm. Is he eligible to play on this under85 kg team?One type of BB gun uses a spring-driven plunger to blow the BB from its barrel. (a) Calculate the force constant of its plunger’s spring if you must compress it 0.150 m to drive the 0.0500kg plunger to a top speed of 20.0m/s. (b) What force must be exerted to compress the spring?(a) The springs of a pickup truck act like a single spring with a force constant of 1.30105N/m. By how much will the truck he depressed by its maximum load of 1000 kg? (b) If the pickup truck has four identical springs, what is the force constant of each?When an 80.0kg man stands on a pogo stick, the spring is compressed 0.120 m. (a) What is the force constant of the spring? (b) Will the spring be compressed more when he hops down the read?A spring has a length of 0.200 m when a 0.300kg mass hangs from it, and a length of 0.750 m when a 1.95-kg mass hangs from it. (a) What is the force constant of the spring? (b) What is The unloaded length of the spring?What is the period of 60.0 Hz electrical power?If your heart rate is 150 beats per minute during strenuous exercise, what is the time per beat in units of seconds?Find the frequency of a tuning fork that takes 2.50103 s to complete one oscillation.A stroboscope is set to flash every 8.00105s. What is the frequency of the flashes?A tire has a tread pattern with a crevice every 2.000 cm. Each crevice makes a single vibration as the tire moves. What is the frequency of these vibrations if the car moves at 30.0 m/s?Engineering Application Each piston of an engine makes a sharp sound every other revolution of the engine. (a) How fast is a race car going if its eight—cylinder engine emits a sound of frequency 750 Hz, given that the engine makes 2000 revolutions per kilometer? (b) At how many revolutions per minute is the engine rotating?A type of cuckoo clock keeps time by having a mass bouncing on a spring, usually something cute like a cherub in a chair. What force constant is needed to produce a period of 0.500 5 for a 0.0150kg mass?If the spring constant of a simple harmonic oscillator is doubled, by what factor will the mass of the system need to change in order for the frequency of the motion to remain the same?A 0.500kg mass suspended from a spring oscillates with a period of 1.50 s. How much mass must be added to the object to change the period to 2.00 s?By how much leeway (both percentage and mass) would you have in the selection of the mass of me object in the previous problem if you did not wish the new period to be greater than 2.01 s or less than 1.99 s?Suppose you attach the object with mass m to a vertical spring originally at rest, and let it bounce up and down. You release the object from rest at the spring's original rest length. (a) Show that the spring exerts an upward force at 2.00 mg on the object at its lowest point. (b) If the spring has a force constant of 10.0 N/m and a 0.25-kg-mass object is set in motion as described. find the amplitude of the oscillations. (c) Find the maximum velocity.A diver on a diving board is undergoing simple harmonic motion. Her mass is 55.0 kg and the period of her motion is 0.800 s. The next diver is a male whose period of simple harmonic oscillation is 1.05 s. What is his mass if the mass at the board is negligible?Suppose a diving beard wi1h no one on it bounces up and down in a simple harmonic motion with a frequency of 4.00 Hz. The board has an effective mass of 10.0 kg. What is the frequency of the simple harmonic motion of a 75.0kg diver on the board?Figure 15.46 This child’s toy relies on springs to keep infants entertained. (credit: By Humboldthead, Flickr) The device pictured in Figure 16.46 entertains infants while keeping them from wandering. The child bounces in a harness suspended from a door frame by a spring constant. (a) If the spring stretches 0.250 m while supporting an 8.0—kg child, what is its spring constant? (b) What is the time for one complete bounce of this child? (c) What is the child's maximum velocity if the amplitude of her bounce is 0.200 m?A 90.0kg skydiver hanging from a parachute bounces up and down with a period of 1.50 s. What is the new period of oscillation when a second skydiver, whose mass is 60.0 kg, hangs from the legs of the first, as seen in Figure 16.47. Figure 16.4? The oscillations of one Skydiver are about to be affected by a second skydiver. (credit: U.S. Army, www.army.mil)What is the leng1h of a pendulum that has a period of 0.500 s?Some people think a pendulum with a period of 1.00 s can be driven with “mental energy“ or psycho kinetically, because its period is the same as an average heartbeat. True or not, what is the length of such a pendulum?What is the period of a 1.00mlong pendulum?How long does it take a child on a swing to complete one swing if her center of gravity is 4.00 m below the pivot?The pendulum on a cuckoo clock is 5.00 cm long. What is its frequency?Two parakeets sit on a swing with their combined center of mass 10.0 cm below the pivot. At what frequency do they swing?(a) A pendulum that has a period of 3.00000 s and that is located where the acceleration due to gravity is 9.79m/s2 is moved to a location where it the acceleration due to gravity is 9.82m/s2. What is its new period? (b) Explain Why so many digits are needed in the value for the period, based on the relation between the period and the acceleration due to gravity.A pendulum with a period of 2.00000 s in one location (g=9.80m/s2) is moved to a new location where the period is now 1.99796 s. What is the acceleration due to gravity at its new location?(a) What is the effect on the period of a pendulum if you double its length? (b) What is the effect on the period of a pendulum if you decrease its length by 5.00%?Find the ratio of the new/old periods of a pendulum if the pendulum were transported from Earth to the Moon, where the acceleration due to gravity is 1.63m/s2.At what rate will a pendulum clock run on me Moon, where the acceleration due to gravity is 1.63 m/s2, if it keeps time accurately on Earth? That is, find the time (in hours) it takes me clock's hum hand to make one revolution on the Moon.Suppose the length of a clock’s pendulum is changed by 1.000%, exactly at noon one day. What time will it read 24.00 hours later, assuming it the pendulum has kept perfect time before the change? Note that there are two answers, and perform the calculation to four—digit precision.If a pendulumdriven clock gains 5.00 s/day, what fractional change in pendulum length must be made for it to keep perfect time?The length of nylon rope from which a mountain climber is suspended has a force constant of 1.40104N/m. (a) What is the frequency at which he bounces, given his mass plus and me mass of his equipment are 90.0 kg? (b) How much would this rope stretch to break the climber’s fall if he treefalls 2.00 m before the rope runs out of slack? Hint: Use conservation of energy. (c) Repeat both parts of this problem in the situation where twice this length of nylon rope is used.Engineering Application Near the top of the Citigroup Center building in New York City, there is an object with mass of 4.00105kg on springs that have adjustable force constants. Its function is to dampen wind—driven oscillations of the building by oscillating at the same frequency as the building is being driven—the driving force is transferred to the object, which oscillates instead of the entire building. (a) What effective force constant should the springs have to make the object oscillate with a period of 2.00 s? (b) What energy is stored in the springs for a 2.00-m displacement from equilibrium?(a) What is me maximum 1nreluzmcity at an 85.0kg person bouncing on a bathroom scale having a force constant of 1.50106N/m, if the amplitude of the bounce is 0.200 cm? (b)What is me maximum energy stored in the spring?A novelty clock has a 0.0100kg mass object bouncing on a spring that has a force constant of 1.25N/m. What is the maximum velocity of me object if me object bounces 3.00 cm above and below its equilibrium position? (b) How many joules of kinetic energy does me object have at its maximum velocity?At what positions is the speed of a simple harmonic oscillator halt its maximum? That is, what values of x/X give v=vmax/2, where X is the amplitude of the motion?A ladybug sits 12.0 cm from the center of a Beatles music album spinning at 33.33 rpm. What is the maximum velocity of its shadow on the wall behind the turntable, it illuminated parallel to the record by the parallel rays of the setting Sun?The amplitude of a lightly damped oscillator decreases by 3.0% during each cycle. What percentage of the mechanical energy of the oscillator is lost in each cycle?How much energy must the shock absorbers of a 1200-kg car dissipate in order to damp a bounce that initially has a velocity 0.800m/s at the equilibrium position? Assume the car returns to its original vertical position.If a car has a suspension system with a force constant of 5.00104N/m, how much energy must me car‘s shocks remove to dampen an oscillation stating with a maximum displacement of 0.0150 m?(a) How much will a spring that has a force constant of 40.0 mm be stretched by an object with a mass of 0.500 kg when hung motionless from the spring? (b) Calculate the decrease in gravitational potential energy of the 0.500kg object when it descends this distance. (c) Part of this gravitational energy goes into the spring. Calculate the energy stored in the spring by this stretch, and compete it with the gravitational potential energy. Explain where the rest of the energy might go.Suppose you have a 0.750kg object on a horizontal surface connected to a spring that has a force constant of 150N/m. There is simple friction between me object and surface with a static coefficient of friction =0.100. (a) How far can the spring be stretched without moving the mass? (b) If the object is set into oscillation with an amplitude twice the distance found in part (a), and me kinetic coefficient of friction is k=0.0850, what total distance does it travel before stopping? Assume it starts at me maximum amplitude.Engineering Application: A suspension bridge oscillates with an effective force constant of 1.00108N/m. (a) How much energy is needed to make it oscillate with an amplitude of 0.100 m? (h) It soldiers march across the bridge with a cadence equal to the bridge’s natural frequency and impart 1.00104J of energy each second, how long does it take for the bridge's oscillations to go from 0.100 m to 0.500 m amplitude?Stems in the South Pacific can create waves that travel all the way to the California coast, which are 12.000 km away. How long does it take them it they travel at 15.0m/s ?Waves on a swimming pool propagate at 0.750m/s. You splash the water at one end of the pool and observe the wave go to the opposite end, reflect, and return in 30.0 s. How far away is the other end of the pool?Wind gusts create ripples on the ocean that have a wavelength at 5.00 cm and propagate at 2.00m/s. What is their frequency?How many times a minute does a boat bob up and down an ocean waves that have a wavelength of 40.0 m and a propagation speed of 5.00m/s ?Scouts at a camp shake the rope bridge may have just crossed and observe the wave crests to be 8.00 m apart. If they shake it the bridge twice per second, what is the propagation speed of the waves?What is the wavelength of the waves you create in a swimming pool if you splash your hand at a rate of 2.00 Hz and the waves propagate at 0.800m/s ?What is the wavelength of an earthquake that shakes you with a frequency of 10.0 Hz and gets to another city 84.0 km away in 12.0 s?Radio waves transmitted through space at 3.00108m/s by the Voyager spacecraft have a wavelength of 0.120 m. What is their frequency?Your ear is capable of differentiating sounds that arrive at the ear just 1.00 ms apart. What is the minimum distance between two speakers that produce sounds that arrive at noticeably different times on a day when the speed of sound is 340m/s ?(a) Seismographs measure the arrival times of earthquakes with a precision of 0.100 s. To get the distance to the epicenter of the quake, they compare the arrival times of S and Pwaves, which travel at different speeds. Figure 16.48) If S and Pwaves travel at 4.00 and 7.20km/s, respectively, in the region considered, how precisely can the distance to the source of the earthquake be determined? (b) Seismic waves from underground detonations of nuclear bombs can be used to locate the test site and detect violations of test bans. Discuss whether your answer to (a) implies a serious limit to such detection. (Note also that the uncertainty is greater if there is an uncertainty in the propagation speeds of the S and P—waves.) Figure 16.48 A seismograph as described in above problem. (credit: Oleg Alexandrov)A car has two horns, one emitting a frequency of 199 Hz and the other emitting a frequency of 203 Hz. What beat frequency do they produce?The middleChammer of a piano hits two strings, producing beats of 1.50 Hz. One of the strings is tuned to 260.00 Hz. What frequencies could the other string have?Two tuning forks having frequencies of 460 and 464 Hz are struck simultaneously. What average frequency will you hear, and what will The beat frequency be?Twin jet engines on an airplane are producing an average sound frequency of 4100 Hz with a beat frequency of 0.500 HZ. What are their individual frequencies?A wave traveling on a Slinky® mat is stretched to 4 m takes 2.4 s to travel the length at me Slinky and back again. (a) What is the speed of the wave? (b) Using the same Slinky stretched to the same length, a standing wave is created which consists of three antinodes and four nodes. At what frequency must the Slinky be oscillating?Three adjacent keys on a piano (F, F—sharp, and G) are stuck simultaneously, producing frequencies of 349, 370, and 392 Hz. What beat frequencies are produced by this discordant combination?Medical Application Ultrasound of intensity 1.50102W/m2 is produced by the rectangular head of a medical imaging device measuring 3.00 by 5.00 cm. What is its power output?The low-frequency speaker of a stereo set hag a surface area of 0.05 m2 and produces 1W 0f acoustical power. What is the intensity at the speaker? If the speaker projects sound uniformly in all directions, at what distance from the speaker is the intensity 0.1W/m2 ?To increase intensity of a wave by a factor of 50, by what factor should the amplitude be increased?Engineering Application A device called an insolation meter is used to measure the intensity of sunlight has an area of 100 cm2 and registers 6.50 w. What is the intensity in W/m2 ?Astronomy Application Energy from the Sun arrives at the top of the Earth’s atmosphere with an intensity of 1.30kW/m2. How long does it take for 1.8109J to arrive on an area of 1.00 m2?Suppose you have a device that extracts energy from ocean breakers in direct proportion to their intensity. If the device produces 10.0 kW of power on a day when the breakers are 1.20 m high, how much will it produce when they are 0.600 m high?Engineering Application (a) A photovoltaic array of (solar cells) is 10.0% ef?cient in gathering solar energy and converting it to electricity. If the average intensity of sunlight on one day is 700W/m2, what area should your array have to gather energy at the rate of 100 W? (b) What is the maximum test of the array if it must pay for itself in two years of operation averaging 10.0 hours per day? Assume that it earns money at the rate of 9.00 (¢ per kilowatthour.A microphone receiving a pure sound tone feeds an oscilloscope, producing a wave on its screen. If the sound intensity is originally 2.00105W/m2, but is turned up until the amplitude increases by 30.0%, what is the new intensity?Medical Application (a) What is the intensity in W/m2 of a laser beam used to burn away cancerous tissue that, when 90.0% absorbed, puts 500 J of energy into a circular spot 2.00 mm in diameter in 4.00 s? (b) Discuss how this intensity compares to the average intensity of sunlight (about 700W/m2 ) and the implications that would have if the laser beam entered your eye. Note how your answer depends on me time duration of the exposure.How do sound vibrations of atoms differ from thermal motion?When sound passes from one medium to another where its propagation speed is different, does its frequency or wavelength change? Explain your answer briefly.Six members at a synchronized swim team weal earplugs to protect themselves against water pressure at depths, but they can still hear the music and perform the combinations in the water perfectly. One day, they were asked to leave the pool so the dive team could practice a few dives, and they tried to practice on a mat, but seemed to have a lot more difficulty. Why might this be?A community is concerned about a plan to bring train service to their downtown from the town's outskirts. The current sound intensity level, even though the rail yard is blocks away, is 70 dB downtown. The mayor assures the public that there will be a difference of only 30 dB in sound in the downtown area. Should the townspeople be concerned? Why?Is the Doppler shift real or just a sensory illusion?Due to eficiency considerations related to its bow wake, the supersonic transport aircraft must maintain a cruising speed that is a constant ratio to the speed of sound (a constant Mach number]. If the aircraft flies from warm air into colder ail, should it increase or decrease its speed? Explain your answer.When you hear a sonic boom, you often cannot see the plane that made it. Why is that?How does an unamplified guitar produce sounds so much more intense than muse of a plucked string held taut by a simple stick?You are given two wind instruments of identical length. One is open at both ends, whereas the other is closed at one end. Which is able to produce the lowest frequency?What is the difference between an overtone and a harmonic? Are all harmonics overtones? Are all overtones harmonics?Why can a hearing test show that your threshold of hearing is 0 dB at 250 Hz, when Figure 17.37 implies that no one can hear such a frequency at less than 20 dB? Figure 17.37 The shaded region represents frequencies and intensity levels found in normal conversational speech. The O-phon line represents the normal hearing threshold, while those at 40 and 60 represent thresholds for people with 40- and 60-phon hearing losses, respectively.If audible sound follows a rule of thumb similar to that for ultrasound, in terms of its absorption, would you expect the high or low frequencies from your neighbor’s stereo to penetrate into your house? How does Hus expectation compare with your experience?Elephants and whales are known to use infrasound to communicate over very large distances. What are the advantages of infrasound for long distance communication?It is more difficult to obtain a high—resolution ultrasound image in the abdominal legion at someone who is overweight than let someone who has a slight build. Explain why this statement is accurate.Suppose you read mat 210dB ultrasound is being used to pulverize cancerous tumors. You calculate me intensity in watts per centimeter squared and find it is unreasonably high (105 W/cm2). What is a possible explanation?When poked by a spear, an operatic soprano lets out a 1200—Hz shriek. What is its wavelength if the speed of sound is 345 m/s?What frequency sound has a 0.10m wavelength when the speed of sound is 340 m/s?Calculate the speed of sound on a day when a 1500 Hz frequency has a wavelength of 0.221 m.(a) What is the speed of sound in a medium where a 100kHz frequency produces a 5.96cm wavelength? (b) Which substance in Table 17.1 is this likely to be?Show mat the speed of sound in 20.0°C air is 343 m/s, as claimed in the text.Air temperature in the Sahara Desert can reach 56.0°C (about 134°F). What is line speed of sound in air at that temperature?Dolphins make sounds in air and water. What is the ratio of the wavelength at a sound in air to its wavelength in seawater? Assume air temperature is 20.0°C.A sonar echo returns to a submarine 1.20 s after being emitted. What is the distance to the object creating the echo? (Assume that the submarine is in me ocean. not in fresh water.)(a) If a submarine’s sonar can measure echo times with a precision of 0.00100 s, what is the smallest difference in distances it can detect? (Assume that the submarine is in the ocean, not in fresh water.) (b) Discuss the limits this time resolution imposes on the ability of the sonar system to detect the size and Shape of the object creating the echo.A physicist a1 a fireworks display times the lag between seeing an explosion and hearing its sound, and finds it to be 0.400 s. (a) How far away is the explosion if air temperature is 24.0°C and if you neglect the time taken for light to reach the physicist? (b) Calculate the distance to the explosion taking the speed of light into account. Note that this distance is negligibly greater.Suppose a bat uses sound echoes to locate its insect prey, 3.00 m away. (See Figure 17.10.) (a) Calculate the echo times for temperatures of 5.00°C and 35.0°C. (b) What percent uncertainty does this cause for the bat in locating the insect? (c) Discuss the significance of this uncertainty and whether it could cause difficulties for the bat. (In practice, the hat continues to use sound as it closes in, eliminating most of any dif?culties imposed by this and other effects, such as motion of the prey.) Figure 17.10 A bat uses sound echoes to find its way about and to catch prey. The time for the echo to return is directly proportional to the distance.What is the intensity in watts per meter squared of 85.0dB sound?The warning tag on a lawn mower states that it produces noise at a level at 91.0 dB. What is this in watts per meter squared?A sound wave traveling in 20°C air has a pressure amplitude of 0.5 Pa. What is the intensity of the wave?What intensity level does the sound in the preceding problem correspond to?What sound intensity level in dB is produced by earphones that create an intensity of 4.00102W/m2 ?Show that an intensity of 1012 W/m2 is the same as 1016 W/cm2.(a) What is the decibel level of a sound that is twice as intense as a 90.0dB sound? (b) What is the decibel level of a sound that is one—?fth as intense as a 90.0—dB sound?(a) What is the intensity of a sound that has a level 7.00 dB lower than a 4.00109W/m2 sound? (b) What is the intensity of a sound that is 3.00 dB higher than a 4.00109W/m2 sound?(a) How much more intense is a sound that has a level 17.0 dB higher man another? (b) If one sound has a level 23.0 dB less than another, what is the ratio of their intensi?es?People with good hearing can perceive sounds as low in level as 8.00 dB at a frequency of 3000 Hz. What is the intensity of this sound in watts per meter squared?If a large housefly 3.0 m away from you makes a noise of 40.0 dB, what is the noise level of 1000 flies at that distance, assuming interference has a negligible effect?Ten cars in a circle at a boom box competition produce a 120dB sound intensity level at the center of me circle. What is the average sound intensity level produced here by each stereo, assuming interference effects can be neglected?The amplitude of a sound wave is measured in terms of its maximum gauge pressure. By what factor does the amplitude of a sound wave increase if the sound intensity level goes up by 40.0 dB?If a sound intensity level of 0 dB at 1000 Hz corresponds to a maximum gauge pressure (sound amplitude) of 109 atm, what is the maximum gauge pressure in a 60dB sound? What is the maximum gauge pressure in a 120dB sound?An 8hour exposure to a sound intensity level of 90.0 dB may cause hearing damage. What energy in joules falls on a 0.800cmdiameter eardrum so exposed?(a) Ear trumpets were never very common, but they did aid people with hearing losses by gathering sound over a large area and concentrating it on the smaller area of the eardrum. What decibel increase does an ear trumpet produce it its sound gathering area is 900 cm2 and the area of the eardrum is 0.500 cm2, but the trumpet only has an eficiency of 5.00% in transmitting the sound to the eardrum? (b) Comment on the usefulness of the decibel increase found in part (a).Sound is more effectively transmitted into a stethoscope by direct contact than through the air, and it is further intensi?ed by being concentrated on the smaller area of the eardrum. It is reasonable to assume that sound is transmitted into a stethoscope 100 times as effectively compared with transmission though the air. What, then, is the gain in decibels produced by a stethoscope that has a sound gathering area at 15.0 cm2, and concentrates the sound onto two eardrums with a total area of 0.900 cm2 with an efficiency of 40.0%?Loudspeakers can produce intense sounds with surprisingly small energy input in spite of their low efficiencies. Calculate the power input needed to produce a 90.0—dB sound intensity level for a 12.0-cm-diameter speaker that has an eficiency of 1.00%. (This value is the sound intensity level right at the Speaker.)(a) What frequency is received by a person watching an oncoming ambulance moving at 110 km/h and emitting a steady 800—Hz sound from its siren? The speed of sound on this day is 345 m/s. (b) What frequency does she receive after the ambulance has passed?(a) At an air show a jet flies directly toward the stands at a speed of 1200 km/h, emitting a frequency of 3500 Hz, on a day when the speed of sound is 342 m/s. What frequency is received by the observers? (b) What frequency do they receive as the plane flies directly away from them?What frequency is received by a mouse just before being dispatched by a hawk flying at it at 25.0 m/s and emitting a screech of frequency 3500 Hz? Take the Speed of sound to be 331 m/s.A spectator at a parade receives an 888-Hz tone from an oncoming trumpeter who is playing an 880—Hz note. At what speed is the musician approaching if the Speed of sound is 338 m/s?A commuter train blows its 200Hz horn as it approaches a crossing. The speed at sound is 335 m/s. (a) An observer waiting at the crossing receives a frequency of 208 Hz. What is the speed of the train? (b) What frequency does the observer receive as the train moves away?Can you perceive the shift in frequency produced when you pull a tuning fork toward you at 10.0 m/s on a day when the speed of sound is 344 m/s? To answer this question, calculate the factor by which the frequency shifts and see if it is greater than 0.300%.Two eagles fly directly toward one another. The first at 15.0 m/s and the second at 20.0 m/s. Both screech, the first one emitting a frequency of 3200 Hz and the second one emitting a frequency of 3800 Hz. What frequencies do they receive if the speed of sound is 330 m/s?What is the minimum speed at which a source must travel toward you for you to be able to hear that its frequency is Doppler shifted? Thai is, what speed produces a shift of 0.300% on a day when the speed of sound is 331 m/s?A “showy" custom—built car has two brass horns that are supposed to produce the same frequency but actually emit 263.8 and 264.5 Hz. What beat frequency is produced?What beat frequencies will be present: (a) If the musical notes A and C are played together (frequencies of 220 and 264 Hz)? (b) If D and F are played together (frequencies at 297 and 352 Hz)? (c) If all four are played together?What beat frequencies result if a piano hammer hits there strings that emit frequencies of 127.8, 128.1, and 128.3 Hz?A piano tuner hears a heat every 2.00 s when listening to a 264.0Hz tuning fork and a single piano string. What are the two possible frequencies of the string?(a) What is the fundamental frequency of a 0.672—m—long tube, open at both ends, on a day when the speed of sound is 344 m/s? (b) What is the frequency of its second harmonic?If a wind instrument, such as a tuba, has a fundamental frequency of 32.0 Hz, what are its first three overtones? It is closed at one end. (The overtones of a real tuba are more complex than this example, because it is a tapered tube.)What are the first three overtones of a bassoon that has a fundamental frequency of 90.0 Hz? It is open at both ends. (The overtones of a real bassoon are more complex man this example, because its double reed makes it act more like a tube closed at one end.)How long must a fiute be in order to have a fundamental frequency of 262 Hz this frequency corresponds to middle C on the evenly tempered chromatic scale) on a day when air temperature is 20.0°C? It is open at both ends.What length should an oboe have to produce a fundamental frequency of 110 Hz on a day when the speed of sound is 343 m/s? It is open at both ends.What is the length of a tube that has a fundamental frequency of 176 Hz and a first overtone of 352 Hz if the speed of sound is 343 m/s?(a) Find the length of an organ pipe closed at one end that produces a fundamental frequency of 256 Hz when air temperature is 18.0°C. (b) What is its fundamental frequency at 25.0°C?By what fraction will the frequencies produced by a wind instrument change when air temperature goes from 10.0°C to 30.0°C? That is, find the ratio of the frequencies at those temperatures.The ear canal resonates like a tube closed at one end. (See Figure 17.39.) If ear canals range in length from 1.80 to 2.60 cm in an average population, what is the range of fundamental resonant frequencies? Take air temperature to be 37.0°C, which is the same as body temperature. How does this result correlate with the intensity versus frequency graph (Figure 17.37 of the human ear? 17.39 The illustration shows the gross anatomy of the human ear. Figure 17.37 The shaded region represents frequencies and intensity levels found in normal conversational speech. The O-phon line represents the normal hearing threshold, while those at 40 and 60 represent thresholds for people with 40- and 60-phon hearing losses, respectively.Calculate the first overtone in an ear canal, which resonates like a 2.40cmlong tube closed at one end, by taking air temperature to be 37.0°C. Is the ear particularly sensitive to such a frequency? (The resonances at the ear canal are complicated by its nonuniform shape, which we shall ignore.)A crude approximation at voice production is to consider the breathing passages and mouth to be a resonating tube closed at one end. (See Figure 17.30.) (a) What is the fundamental frequency if the tube is 0.240-m long, by taking air temperature to be 37.0°C? (b) What would this frequency become it the person replaced the air with helium? Assume the same temperature dependence for helium as for air. Figure 17.30 The throat and mouth form an air column closed at one end that resonates in response to vibrations in the voice box. The spectrum of overtones and their intensities vary with mouth shaping and tongue position to form different sounds. The voice box can be replaced with a mechanical vibrator, and understandable speech is still possible. Variations in basic shapes make different voices recognizable.(a) Students in a physics lab are asked to find the length of an air column in a tube closed at one end that has a fundamental frequency of 256 Hz. They hold the tube vertically and fill it with water to the top, then lower the water while a 256—Hz tuning fork is rung and listen for the first resonance. What is the air temperature if the resonance occurs for a length of 0.336 m? (b) At what length will they observe the second resonance (first overtone)?What frequencies will a 1.80-m—long tube produce in the audible range at 20.0°C if: (a) The tube is closed at one end? (b) It is open at both end?The factor of 1012 in the range of intensities to which the ear can respond, from threshold to that causing damage after brief exposure, is truly remarkable. If you could measure distances over the same range with a single instrument and the smallest distance you could measure was 1 mm, what would the largest be?The frequencies to which the ear responds vary by a factor of 103. Suppose the speedometer on your car measured speeds differing by the same factor of 103, and the greatest speed it reads is 90.0 mi/h. What would be the slowest nonzero speed it could read?What are the closest frequencies to 500 Hz that an average person can clearly distinguish as being different in frequency from 500 Hz? The sounds are not present simultaneously.Can the average person tell that a 2002-Hz sound has a different frequency than a 1999-Hz sound without playing them simultaneously?If your radio is producing an average sound intensity level of 85 dB, what is the next lowest sound intensity level that is clearly less intense?Can you tell that your roommate turned up the sound on the TV if its average sound intensity level goes from 70 to 73 dB?Based on the graph in Figure 17.36, what is the threshold of hearing in decibels for frequencies of 60, 400, 1000, 4000, and 15,000 Hz? Note that many AC electrical appliances produce 60 Hz, music is commonly 400 Hz, a reference frequency is 1000 Hz, your maximum sensitivity is near 4000 Hz, and many older TVs produce a 15,750 Hz whine. Figure 17.36 The relationship of loudness in phons to intensity level (in decibels) and intensity (in watts per meter squared) for persons with normal hearing. The curved lines are equal-loudness curves—all sounds on a given curve are perceived as equally loud. Phons and decibels are defined to be the same at 1000 Hz.What sound intensity levels must sounds of frequencies 60,3000, and 8000 Hz have in order to have the same loudness as a 40dB sound of frequency 1000 Hz (that is, to have a loudness of 40 phons)?What is me approximate sound intensity level in decibels of a 600Hz tone if it has a loudness of 20 phons? If it has a loudness of 70 phons?(a) What are the loudnesses in phons of sounds having frequencies of 200, 1000, 5000, and 10,000 Hz. if they are all at the same 60.0dB sound intensity level? (b) If may are all at 110 dB? (c) If they are all at 20.0 dB?Suppose a person has a 50—UB hearing loss at all frequencies. By how many factors of 10 will low—intensity sounds need to be ampli?ed to seem normal to this person? Note that smaller amplification is appropriate for more intense sounds to avoid further hearing damage.If a woman needs an amplification of 5.01012 times we threshold intensity to enable her to hear at all frequencies, what is her overall hearing loss in dB? Note that smaller amplification is appropriate for more intense sounds to avoid further damage to her hearing from levels above 90 dB.(a) What is the intensity in watts per meter squared of a just barely audible ZUD—Hz sound? (b) What is the intensity in watts per meter squared of a barely audible 4000—Hz sound?(a) Find the intensity in watts per meter squared of a 60.0Hz sound having a loudness of 60 phons. (b) Find the intensity in watts per meter squared of a 10,000—Hz sound having a loudness of 60 phons.A person has a hearing threshold 10 dB above normal at 100 Hz and 50 dB above normal at 4000 Hz. How much more intense must a l00—Hz tone be than a 4000-Hz tone if they are both barely audible to this person?A child has a hearing loss of 60 dB near 5000 Hz, due to noise exposure, and normal hearing elsewhere. How much more intense is a 5000—Hz tone than a 400-Hz tone if they are both barely audible to the child?What is the ratio of intensi?es of two sounds of identical frequency if the first is just barely discernible as louder to a person than the second?What is the sound intensity level in decibels of ultrasound of intensity 105 W/m2, used to pulverize tissue during surgery?Is 155—dB ultrasound in the range at intensities used for deep heating? Calculate the intensity of this ultrasound and compare this intensity with values quoted in the text.Find the sound intensity level in decibels of 2.00102W/m2 ultrasound used in medical diagnostics.The time delay between transmission and the arrival of the reflected wave of a signal using ultrasound traveling through a piece of fat tissue was 0.13 ms. At what depth did this reflection occur?In the clinical use of ultrasound, transducers are always coupled to the skin by a thin layer at gel or oil, replacing the air that would otherwise exist between the transducer and the skin. (a) Using the values of acoustic impedance given in Table 17.5 calculate the intensity refiection coef?cient between transducer material and air. (b) Calculate the intensity refiection coefficient between transducer material and gel (assuming for this problem that its acoustic impedance is identical to that of water). (c) Based on the results at your calculations, explain why the gel is used.(a) Calculate the minimum frequency of ultrasound that will allow you to see details as small as 0.250 mm in human tissue. (b) What is the effective depth to which this sound is effective as a diagnostic probe?(a) Find the size of the smallest detail observable in human tissue with 20.0-MHz ultrasound. (b) Is its effective penetration depth great enough to examine the entire eye (about 3.00 cm is needed)? (c) What is the wavelength of such ultrasound in 0°C air?(a) Echo times are measured by diagnostic ultrasound scanners to determine distances to re?ecting surfaces in a patient. What is the difference in echo times for tissues that are 3.50 and 3.60 cm beneath the surface? (This difference is the minimum resolving time for the scanner to see details as small as 0.100 cm, or 1.00 mm. Discrimination of smaller time differences is needed to see smaller details.) (b) Discuss whether the period T at this ultrasound must be smaller than the minimum time resolution. If so, what is the minimum frequency of the ultrasound and is that out of the normal range for diagnostic ultrasound?(a) How far apart are two layers of tissue that produce echoes having round-trip times (used t0 measure distances) that differ by 0.750s ? (b) What minimum frequency must the ultrasound have to see detail this Small?(a) A bat uses ultrasound to find its way among trees. If this bat can detect echoes 1.00 ms apart, what minimum distance between objects can it detect? (b) Could this distance explain the difficulty that bats have finding an open door when they accidentally get into a house?A dolphin is able to tell in the dark that the ultrasound echoes received from two sharks come from two different objects only it the sharks are separated by 3.50 m, one being that much farther away than the other. (a) If the ultrasound has a frequency of 100 kHz, show this ability is not limited by its wavelength. (b) If this ability is due to the dolphin's ability to detect the arrival times of echoes, what is the minimum time difference the dolphin can perceive?A diagnostic ultrasound echo is re?ected from moving blood and returns with a frequency 500 Hz higher than its original 2.00 MHZ. What is the velocity of the bleed? (Assume that the frequency of 2.00 MHz is accurate to seven significant figures and 500 Hz is accurate to three significant figures.)Ultrasound reflected from an oncoming bloodstream mat is moving at 30.0 cm/s is mixed with the original frequency of 2.50 MHZ to produce beats. What is the beat frequency? (Assume than the frequency of 2.50 MHz is accurate to seven significant figures.)There are very large numbers of charged particles in most objects. Why, then, don't most objects exhibit static electricity?Why do most objects tend to contain nearly equal numbers of positive and negative charges?An eccentric inventor attempts to levitate by first placing a large negative charge on himself and then putting a large positive charge on the ceiling of his workshop. Instead, while attempting to place a large negative charge on himself, his clothes fly off. Explain.If you have charged an electroscope by contact with a positively charged object, describe how you could use it to determine the charge of other objects. Specifically, what would the leaves of the electroscope do if other charged objects were brought near its knob?When a glass rod is rubbed with silk, it becomes negativeyet both attract dust. Does the dust have a third type of charge that is attracted to both positive and negative? Explain.Why does a car always attract dust right after it is polished? (Note that car wax and car tires are insulators.)Describe how a positively charged object can be used to give another object a negative charge. What is the name of this process?What is grounding? What effect does it have on a charged conductor? On a charged insulator?Figure 18.43 shows the charge distribution in a water molecule, which is called a polar molecule because it has an inherent separation of charge. Given water's polar character, explain what effect humidity has on removing excess charge from objects. Figure 18.43 Schematic representation of the outer electron cloud of a neutral water molecule. The electrons spend more time near the oxygen than the hydrogens, giving a permanent charge separation as shown. Water is thus a polar molecule. It is more easily affected by electrostatic forces than molecules with uniform charge distributions.Using Figure 18.43, explain, in terms of Coulomb's law, why a polar molecule (such as in Figure 18.43) is attracted by both positive and negative charges Figure 18.43 Schematic representation of the outer electron cloud of a neutral water molecule. The electrons spend more time near the oxygen than the hydrogens, giving a permanent charge separation as shown. Water is thus a polar molecule. It is more easily affected by electrostatic forces thanGiven the polar character of water molecules, explain how ions in the air form nucleation centers for rain droplets.Why must the test charge q in the definition of the electric field be vanishingly small?Are the direction and magnitude of the Coulomb force unique at a given point in space? What about the electric field?Compare and contrast the Coulomb force field and the electric field. To do this, make a list of five properties for the Coulomb force field analogous to the five properties listed for electric field lines. Compare each item in your list of Coulomb force field properties with those of the electric field—are they the same or different? (For example, electric field lines cannot cross. Is the same true for Coulomb field lines?)Figure 18.44 shows an electric field extending over three regions, labeled I, II, and III. Answer the fallowing questions, (a) Are there any isolated charges? If so, in what region and what are their signs? (b) Where is the field strongest? (c) Where is it weakest? (d) Where is the field the most uniform?A cell membrane is a thin layer enveloping a cell. The thickness of the membrane is much less than the size of the cell. In a static situation the membrane has a charge distribution of —2.5 10-6 C/m2 on its inner surface and +2.5 106 C/m2 on its outer surface. Draw a diagram of the cell and the surrounding cell membrane. Include on this diagram the charge distribution and the corresponding electric field. Is there any electric field inside the cell? Is there any electric field outside the cell?Is the object in Figure 18.45 a conductor or an insulator? Justify your answer.