Physics 20 Unit D Assessment

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Physics 20: Unit D Oscillatory Motion and Mechanical Waves /52 At the beginning of this unit, you were given some “I can” statements and other “Questions” as part of “Questions You Should Be Able to Answer For This Unit” document. Your task for this assessment is to find an example question (from any source) that requires the information in each “Question” listed in that document. You’ll then explain how to answer each question, showing all your work, and ultimately, answer the question. You’ll be graded on each question with the following criteria: 1 point Explain how the question relates to the “Questions You Should Be Able to Answer For This Unit” question. 1 point Correct final answer for the question 2 points Relevant formula and work shown, or relevant concepts explained for how to get the answer Some questions might answer multiple “Questions” in this document. While you can use the same question more than once, you will need to re-explain how the question answers that addresses “Question” Remember, this assignment is worth 20% of your grade for this unit, so put a considerable amount of effort into this assignment. 1. Using the terms period and frequency, how can oscillatory motion be described? A student pulls the bob of an ideal pendulum and releases it. After 120 seconds, the student observes that the bob has returned to its pulled position 30 times. What is the period and frequency? The motion of a pendulum is an example of oscillatory motion. Its period is the amount of time that it takes the pendulum to complete one cycle, while its frequency is the number of complete cycles in one second. In other words, the period and frequency are reciprocals of one another. So, T= 120 s /30 c =4.0 s(s/c) f = 1/T = ¼ =0.25 Hz (c/s) 2. What is simple harmonic motion?

spring with a spring constant of 25 N/m is pulled 2.0 m to the right. What is the restoring force? Simple harmonic motion is a special type of oscillatory motion where the restoring force is directly proportional to the displacement. According to this principle, F = -kx. So, F = -(25 N/m x 2.0 m) =-50 N. This means, the restoring force is 50 N to the left. 3. Mathematically, what is the relationship between displacement, acceleration, velocity and time for simple harmonic motion for a mass-spring system? A student attaches a small object of mass 2.3 kg to a horizontal spring that's attached to the wall. The student pulls the object on the spring, and notices that the speed of the object when it is 20 cm from its equilibrium position is 1.5 m/s. Ignoring friction, how much did the student pull the object? Calculate the period, maximum speed and maximum acceleration. Solving this question requires an understanding of the change that occurs in the acceleration, velocity and displacement of a mass-spring system as it undergoes SHM, and also conservation of energy. a)At any point, the mechanical energy, which is the sum of Ep and Ek remains the same. So, when x = 10 cm, Em = ½ (38 N/m)(0.2m)^2+ ½(2.3kg)(1.5m/s)^2= 3.3475J When x is maximum, Ek = 0, So Em = Ep = ½kx^2, x= (2Em/k)^½ x = (2x3.3475/38N/m)^½= 0.4197 m or ∼ 42 cm b)T = 2π(m/k)½= 2π(2.3kg/38N/m) =0.38 s c)When speed is maximum, x = 0, Ep = 0. So Em=Ek=½mv^2 v=(2Em/m)^½=(2x3.3475J/2.3kg)^½=1.7 m/s d)Maximum acceleration occurs when x is maximum (x = 0.4197 m). ma = -kx, a = -kx/m a =-(38N/m)(0.4197m)/2.3kg = 6.9 m/s 4. Mathematically, what is the relationship between displacement, acceleration, velocity and time for simple harmonic motion for a pendulum? A simple pendulum consisting of a bob attached to a cord oscillates in a vertical plane with a period of 1.45 s. If the maximum velocity of the bob is 0.40 m/s, determine the amplitude in degrees, and the maximum acceleration of the bob. T = 2π(l/g)^½, l = gT^2/4π^2= (9.81)(1.45)^2/4π^2= 0.52245 m According to the law of conservation of energy, the total mechanical energy of the pendulum is always the same. At the maximum displacements, Ek = 0, and Em = mgh. At equilibrium, Ep =0, and Em = ½mv^2. So, mgh = ½mv^2, h = v^2/2g = 0.4^2/(2x9.81) = 0.008154943 m

5. Mathematically, what is the relationship between gravitational potential energy, kinetic energy and the total mechanical energy of a mass system undergoing simple harmonic motion? Question #4 and the way it was solved answered this.To find the maximum height, we used the principle that total mechanical energy is always the same, and therefore maximum Ep and maximum Ek are equal. 6. What is mechanical resonance? -Which of the following is an example of mechanical resonance? A. The change in frequency of a fire engine's siren when it passes. B. A wine glass shatters when someone sings at the right resonance frequency of the glass. C. A pendulum swings at a constant period. D. The echo you hear when you clap in an empty room. -Mechanical resonance is the increase in the amplitude of oscillation of a system as a result of a forced frequency that matches its resonant frequency. Choice A is an example of a doppler effect. Choice C is SHM. Choice D is echo, which is the result of sound waves being reflected. The wineglass in choice B breaks because the frequency of the sound waves of the song matches the resonant frequency of the wineglass, and therefore increases the amplitude of the oscillation of the glass and eventually breaks it. 7. Making reference to the direction of motion of the medium and the direction of propagation, what are longitudinal waves? What are transverse waves? -Which of the following are longitudinal waves? Which are transverse waves? In each case, what's the relationship between the direction of propagation of the wave and motion of the medium? A. A ripple moving across the surface of a pond B. A whip cracking C. The movement of the rungs of a spring as it bounces D. Sound waves in air -Choice A and B are examples of transverse waves. The water and the whip move perpendicular to the propagation of the wave. Choice C and D are longitudinal waves because both the spring and the air molecules are compressed and expanded, parallel to the propagation.

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8. How do the terms wavelength, velocity, period, frequency, amplitude, wave front and ray apply to transverse waves? How do they apply to longitudinal waves? 1)In the picture below, the transverse waves are traveling to the right. An observer notes that 5 waves pass by point P in 10 seconds. -Solve for amplitude, wavelength, frequency, period, and speed. -Amplitude is the distance from the midpoint (equilibrium) to the crest, A = 1.5 m, Wavelength is the distance between two consecutive crests λ = 2 m, f = 5 / 10 = 0.5 Hz, T = 10 / 5 = 2 s. v = λf =2 m x 0.5 Hz = 1 m/s 2)A certain sound wave in air has a speed of 340 m/s and wavelength of A certain sound wave in air has a speed of 340 m/s and wavelength of 1.70 m, calculate the frequency and the period. -f = v / λ = 340 m/s / 1.7 m = 200 Hz -T = 1 / f = 1/200 = 5.00 x 10^-3s 9. How does the speed of the wave differ depending on the characteristics of the medium? Which affects the speed, the medium or the source of the wave? How? -The speed of the wave depends on the medium, and that's because the tension of the medium determines the wavelength. The bigger the tension, the bigger the speed. 10. Mathematically, what are the effects of changing one or more variables in the universal wave equation? -The period of a sound wave of a radio is 1.5 x 10^3s. At the same time Dave is listening to the radio, he hears a fire engine siren which has a frequency of 5 times that of the radio. If the speed the sound in air is 330 m/s, what is the wavelength of the siren? -The question uses the universal wave equation, and explores how the change in one variable affects others. T1 = 1.5 x 10^3s, v1 = v2 = 330 m/s f2 = 5f1, λ2 = ? v2 = λf, λ= v2/f2 = v2/5f1 f1 = 1/T1 = 1/(1.5 x 10^3s) = 666.667 Hz λ= 330 m/s / (5 x 666.667 Hz) = 9.9 x 10^2m

11. What are the conditions needed for constructive interference? What are the conditions needed for destructive interference? How do these relate to acoustic resonance? - The diagram shows a tuning fork vibrating over an air column closed at one end by water. If the speed of sound in air is 343 m/s and the first resonance occurs at 8.00 cm, what is the frequency of the tuning fork? What is the length of the air column for the next two harmonics - a standing wave in an air column is created by constructive and destructive interferences. Constructive interferences occur when crests add together (in a standing wave, they form antinodes), and destructive interferences occur when a crest and a trough add together (in a standing waves, they form fixed nodes). For acoustic resonance to occur, a node must be located at the closed end, and an antinode must be located at the open end. -If the first resonance occurs at 8.00cm of the tube, there must be an antinode, which starts at L = ¼λ. So, ¼λ = 8.00 cm, λ = 32 cm. f = v/λ = 343 m/s / 0.32 m =1.07 x 10^3Hz -The next two harmonics occur when L = ¾λ and L = 5/4λ. So, L = ¾(32cm) =25.5 cm and L = 5/4(32cm) = 40.0 cm 12. What is the Doppler effect? How can it be described mathematically? -While standing near a railroad crossing, Kasie hears a train horn. The frequency of the horn is 400 Hz. If the train is traveling at 25 m/s and the speed of sound in air is 345 m/s, what is the frequency Kasie hears when a) the train is approaching b) after it has passed? -The doppler effect is the apparent change in frequency of a wave when the source of the wave is in motion relative to an observer. In this case, the source (train) moves both toward and away from the observer (Kasie). -a) When the train is approaching her, fd = (vw / (vw - vs)) fs = (345 / (345 - 25) ) 400 =431 Hz -b) After the train has passed, fd = (vw / (vw + vs)) fs = (345 / (345 + 25) ) 400 =373 Hz

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