
Concept explainers
(a)
To calculate: The period and frequency of the waves on string.
(a)

Answer to Problem 102P
The period
Explanation of Solution
Given:
Frequency =
Amplitude =
Linear mass density =
Tension =
Formula used:
Theperiod and frequency of the waves on string can be calculated as:
Where,
Calculation:
The frequency of the waves on the string is the similar as that of frequency of the tuning fork and their period is the reciprocal of the frequency.
The frequency of the wave given is:
The period of the wave on the wire is the reciprocal of their frequency:
Conclusion:
Thus, the period
(b)
To calculate: The speed of the wave.
(b)

Answer to Problem 102P
The speed of the wave
Explanation of Solution
Given:
Frequency =
Amplitude =
Linear mass density =
Tension =
Formula used:
For wave speed formula used is:
Where,
Calculation:
By using the tension and the linear density, wave speed can be calculated.
Relate the speed of the waves to the tension in string and linear density:
Conclusion:
Thus, the speed of the wave
(c)
To calculate: The wavelength and wave number.
(c)

Answer to Problem 102P
The wavelength
Explanation of Solution
Given:
Frequency =
Amplitude =
Linear mass density =
Tension =
Formula used:
Where,
Sound’s speed:
Frequency of wave:
The wavelength:
Calculation:
By using the frequency and the speed of the waves and the wave number The wavelength can be determined.
Relate the wavelength and wave no to the speed and frequency of the wave:
Where,
After substituting the values,
Therefore,
Now, evaluate the wave number using wave length:
Hence,
Conclusion:
Thus, the wavelength
(d)
To calculate: Suitable wave function for the wave on the string.
(d)

Answer to Problem 102P
The suitable wave function is
Explanation of Solution
Given:
Frequency =
Amplitude =
Linear mass density =
Tension =
Formula used:
For wave speed formula used is:
Where,
Calculation:
The general form of the wave function for waves on a string is
So, with the help of
Initially, find out the angular frequency of the waves:
Now, put
Conclusion:
Thus, the suitable wave function is
(e)
To calculate: max speed and acceleration point on the string.
(e)

Answer to Problem 102P
The max speed
Explanation of Solution
Given:
Frequency =
Amplitude =
Linear mass density =
Tension =
Formula used:
For max speed formula used is:
Where,
Calculation:
The max speed and acceleration ofa point on the string can be determined from the angular frequency and amplitude ofthe waves.
Relate the max speed of apoint on the string to the amplitude of the waves and tuning fork’s the angular frequency:
Now, expression for the max acceleration of string point in terms of the amplitude and angular frequency of the tuning fork is:
Put the values to get max acceleration:
Conclusion:
Thus, the max speed
(f)
To calculate: minimum average rate of energy supplied to fork.
(f)

Answer to Problem 102P
The minimum average rate of energy
Explanation of Solution
Given:
Frequency =
Amplitude =
Linear mass density =
Tension:
Formula used:
For minimum average rate of energyformula used is:
Where,
Calculation:
The expression for the minimum average power essential to keep the tuning fork oscillating at steady amplitude in terms of linear density of string, the amplitude of its vibrations and wave speed:
Where,
Now, substitute the values in the equation:
Conclusion:
Thus, the minimum average rate of energy
Want to see more full solutions like this?
Chapter 15 Solutions
Physics for Scientists and Engineers, Vol. 1
- Consider the series M8 3 ཱ|༤༠ n=0 5n a. Find the general formula for the sum of the first k terms. Your answer should be in terms of k. Sk=3 1 5 5 k b. The sum of a series is defined as the limit of the sequence of partial sums, which means k 3 5n 1- = lim 3 k→∞ n=0 4 15 4 c. Select all true statements (there may be more than one correct answer): A. The series is a geometric series. B. The series converges. C. The series is a telescoping series (i.e., it is like a collapsible telescope). D. The series is a p-series.arrow_forwardA uniform ladder of length L and weight w is leaning against a vertical wall. The coefficient of static friction between the ladder and the floor is the same as that between the ladder and the wall. If this coefficient of static friction is μs : 0.535, determine the smallest angle the ladder can make with the floor without slipping. ° = A 14.0 m uniform ladder weighing 480 N rests against a frictionless wall. The ladder makes a 55.0°-angle with the horizontal. (a) Find the horizontal and vertical forces (in N) the ground exerts on the base of the ladder when an 850-N firefighter has climbed 4.10 m along the ladder from the bottom. horizontal force magnitude 342. N direction towards the wall ✓ vertical force 1330 N up magnitude direction (b) If the ladder is just on the verge of slipping when the firefighter is 9.10 m from the bottom, what is the coefficient of static friction between ladder and ground? 0.26 × You appear to be using 4.10 m from part (a) for the position of the…arrow_forwardYour neighbor designs automobiles for a living. You are fascinated with her work. She is designing a new automobile and needs to determine how strong the front suspension should be. She knows of your fascination with her work and your expertise in physics, so she asks you to determine how large the normal force on the front wheels of her design automobile could become under a hard stop, ma when the wheels are locked and the automobile is skidding on the road. She gives you the following information. The mass of the automobile is m₂ = 1.10 × 103 kg and it can carry five passengers of average mass m = 80.0 kg. The front and rear wheels are separated by d = 4.45 m. The center of mass of the car carrying five passengers is dCM = 2.25 m behind the front wheels and hcm = 0.630 m above the roadway. A typical coefficient of kinetic friction between tires and roadway is μk 0.840. (Caution: The braking automobile is not in an inertial reference frame. Enter the magnitude of the force in N.)…arrow_forward
- John is pushing his daughter Rachel in a wheelbarrow when it is stopped by a brick 8.00 cm high (see the figure below). The handles make an angle of 0 = 17.5° with the ground. Due to the weight of Rachel and the wheelbarrow, a downward force of 403 N is exerted at the center of the wheel, which has a radius of 16.0 cm. Assume the brick remains fixed and does not slide along the ground. Also assume the force applied by John is directed exactly toward the center of the wheel. (Choose the positive x-axis to be pointing to the right.) (a) What force (in N) must John apply along the handles to just start the wheel over the brick? (No Response) N (b) What is the force (magnitude in kN and direction in degrees clockwise from the -x-axis) that the brick exerts on the wheel just as the wheel begins to lift over the brick? magnitude (No Response) KN direction (No Response) ° clockwise from the -x-axisarrow_forwardAn automobile tire is shown in the figure below. The tire is made of rubber with a uniform density of 1.10 × 103 kg/m³. The tire can be modeled as consisting of two flat sidewalls and a tread region. Each of the sidewalls has an inner radius of 16.5 cm and an outer radius of 30.5 cm as shown, and a uniform thickness of 0.600 cm. The tread region can be approximated as having a uniform thickness of 2.50 cm (that is, its inner radius is 30.5 cm and outer radius is 33.0 cm as shown) and a width of 19.2 cm. What is the moment of inertia (in kg. m²) of the tire about an axis perpendicular to the page through its center? 2.18 x Sidewall 33.0 cm 30.5 cm 16.5 cm Treadarrow_forwardA person on horseback is on a drawbridge which is at an angle = 20.0° above the horizontal, as shown in the figure. The center of mass of the person-horse system is d = 1.35 m from the end of the bridge. The bridge is l = 7.00 m long and has a mass of 2,300 kg. A cable is attached to the bridge 5.00 m from the frictionless hinge and to a point on the wall h = 12.0 m above the bridge. The mass of person plus horse is 1,100 kg. Assume the bridge is uniform. Suddenly (and most unfortunately for the horse and rider), the ledge where the bridge usually rests breaks off, and at the same moment the cable snaps and the bridge swings down until it hits the wall. ÚI MAJI A TLA MAJA AUTA (a) Find the angular acceleration (magnitude, in rad/s²) of the bridge once it starts to move. 2.22 Use the rotational analogue of Newton's second law. The drawbridge can be modeled as a rod, with rotation axis about one end. rad/s² (b) How long (in s) does the horse and rider stay in contact with the bridge…arrow_forward
- Two long, parallel wires carry currents of I₁ = 2.70 A and I2 = 4.85 A in the directions indicated in the figure below, where d = 22.0 cm. (Take the positive x direction to be to the right.) 12 (a) Find the magnitude and direction of the magnetic field at a point midway between the wires. magnitude direction 3.91 270 μπ ⚫ counterclockwise from the +x axis (b) Find the magnitude and direction of the magnetic field at point P, located d = 22.0 cm above the wire carrying the 4.85-A current. magnitude direction Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. μT The response you submitted has the wrong sign.° counterclockwise from the +x axisarrow_forwardO Macmillan Learning The mass of a particular eagle is twice that of a hunted pigeon. Suppose the pigeon is flying north at Vi2 = 16.1 m/s when the eagle swoops down, grabs the pigeon, and flies off. At the instant right before the attack, the eagle is flying toward the pigeon at an angle 0 = 64.3° below the horizontal and a speed of Vi,1 = 37.9 m/s. What is the speed of of the eagle immediately after it catches its prey? What is the magnitude & of the angle, measured from horizontal, at which the eagle is flying immediately after the strike? Uf = II x10 TOOLS Vi.1 Vi,2 m/sarrow_forwardWhat is the equivalent resistance if you connect a 1.7 Ohm, a 9.3 Ohm, and a 22 Ohm resistor in series? (Give your answer as the number of Ohms.)arrow_forward
- Three wires meet at a junction. One wire carries a current of 5.2 Amps into the junction, and a second wire carries a current of 3.7 Amps out of the junction. What is the current in the third wire? Give your answer as the number of Amps, and give a positive number if the current in that wire flows out of the junction, or a negative number if the current in that wire flows into the junction.arrow_forwardWhat is the equivalent resistance if you connect a 4.5 Ohm, a 6.8 Ohm, and a 15 Ohm resistor in parallel? (Give your answer as the number of Ohms.)arrow_forwardSuppose a heart defibrillator passes 10.5 Amps of current through a patient's torso for 5.0 x 10-3 seconds in order to restore a regular heartbeat. The voltage across the defibrillator is 9800 volts for the entire time that current is flowing. If 7.25 kg of body tissue is involved, with a specific heat of 3500 J/(kg°C), then what is the resulting temperature increase of the person's torso? (Give your answer as the number of degrees C.)arrow_forward
- University Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice UniversityPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningGlencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-HillPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning





