Problem Set 11Due: 5/24/11, Tuesday

Chapter 16: Waves - IExercises & Problems: 9, 19, 26, 33, 41, 50, 55, 63

Chapter 17: Waves-IIExercises & Problems: 23, 38, 55, 60

*Problem Set Quiz #7 on Tuesday, May 24th*

Problem AIs it possible to have a longitudinal wave on a stretched string? Why or why not? Is it possible to have a transverse wave on a steel rod? Again, why or why not? If your answer is yes in either case, explain how you would create such a wave.

Problem BViolins are short instruments, while cellos and basses are long. In terms of the frequency of the waves they produces, explain why this is so.

Problem CA large church has part of the organ in the front of the church and part in the back. A person walking rapidly down the aisle while both segments are playing at once reports that the two segments sound out of tune. Why?

Problem DA sound source and a listener are both at rest on the earth, but a strong wind is blowing from the source toward the listener. Is there a Doppler effect? Why or why not?

Problem EWhen you inhale helium, your voice becomes high and squeaky. Why?

Problem FA sound source and a listener are both at rest on the earth, but a strong wind is blowing from the source toward the listener. Is there a Doppler effect? Why or why not?

Problem 16.7 A transverse sinusoidal wave is moving along a string in the positive direction of an x axis with a speed of 80 m/s. At t = 0, the string particle at x = 0 has a transverse displacement of 4.0 cm from its equilibrium position and is not moving. The maximum transverse speed of the string particle at x = 0 is 16 m/s. (a) What is the frequency of the wave? (b) What is the wavelength of the wave? If the wave equation is of the form y = ymsin(kx + t + ), what are (c) ym, (d) k, (e) , (f) , and (g) the correct choice of sign in front of .

Problem 16.9Two sinusoidal waves with the same amplitude of 9.00 mm and the same wavelength travel together along a string that is stretched along an x axis. Their resultant wave is shown twice in the figure, as valley A travels in the negative direction of the x axis by distanced = 56.0 cm in 8.0 ms. The tick marks along the axis are separated by 10 cm, and height H is 8.0 mm. Let the equation for one wave be of the form y =

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ymsin(kx ± t + ), where = 0 and you must choose the correct sign in front of . For the equation for the other wave, what are (a) ym, (b) k, (c) , (d) , and (e) the sign in front of ?

Problem 16.17The linear density of a string is 1.6 × 10-4 kg/m. A transverse wave on the string is

described by the equation . What are (a) the wave

speed and (b) the tension in the string?

Problem 16.26A string along which waves can travel is 2.70 m long and has a mass of 260 g. The tension in the string is 36.0 N. What must be the frequency of traveling waves of amplitude 7.70 mm for the average power to be 85.0 W?

Problem 16.43What are (a) the lowest frequency, (b) the second lowest frequency, and (c) the third lowest frequency for standing waves on a wire that is 10.0 m long, has a mass of 100 g, and is stretched under a tension of 250 N?

Problem 16.52A rope, under a tension of 200 N and fixed at both ends, oscillates in a second-harmonic standing wave pattern. The displacement of the rope is given by y = (0.10m) sin(x/2) sin(12t), where x = 0 at one end of the rope, x is in meters, and t is in seconds. What are (a) the length of the rope, (b) the speed of the waves on the rope, and (c) the mass of the rope? (d) If the rope oscillates in a third-harmonic standing wave pattern, what will be the period of oscillation?

Problem 16.57A generator at one end of a very long string creates a wave given by

and a generator at the other end creates the

wave . Calculate the (a) frequency, (b)

wavelength, and (c) speed of each wave. For x ≥ 0, what is the location of the node having the (d) smallest, (e) second smallest, and (f) third smallest value of x? For x ≥ 0, what is the location of the antinode having the (g) smallest, (h) second smallest, and (i) third smallest value of x?

Problem 16.67Two sinusoidal waves, identical except for phase, travel in the same direction along a

string, producing a net wave , with x in meters and t

in seconds. What are (a) the wavelength of the two waves, (b) the phase difference between them, and (c) their amplitude ym?

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Problem 17.23Two point sources S1 and S2 emit sound of wavelength = 2.00m. The emissions are isotropic and in phase, and the separation between the sources is d = 16.0m. At any point P on the x axis, the wave from S1 and the wave from S2 interfere. When P is very far away what are (a) the phase difference between the arriving waves from S1 and S2 and (b) the type of interference they produce? Now move point P along the x axis toward S1. (c) Does the phase difference between the waves increase or decrease? At what distance x do the waves have a phase difference of (d) 0.50, (e) , and (f) 1.5?

Problem 17.38The water level in a vertical glass tube 1.00 m long can be adjusted to any position in the tube. A tuning fork vibrating at 686 Hz is held just over the open top end of the tube, to set up a standing wave of sound in the air-filled top portion of the tube. (That air-filled top portion acts as a tube with one end closed and the other end open.) (a) For how many different positions of the water level will sound from the fork set up resonance in the tube’s air-filled portion, which acts as a pipe with one end closed (by the water) and the other end open? What are the (b) least and (c) second least water heights in the tube for resonance to occur?

Problem 17.55A whistle of frequency 540 Hz moves in a circle of radius 60.0 cm at an angular speed of 15.0 rad/s. What are the (a) lowest and (b) highest frequencies heard by a listener a long distance away, at rest with respect to the center of the circle?

Problem 17.60A stationary motion detector sends sound waves of frequency 0.150 MHz toward a truck approaching at a speed of 45.0 m/s. What is the frequency of the waves reflected back to the detector?

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