Q: A metal bar has a length of 1.5 m and a density of $$6400\ \mathrm{kg/m^3$}. $$Sound waves take $$3.9 \times 10$$^{-4}$$ s to travel along the length of the bar. What is the Young’s modulus for this metal?

$$Y = 9.47 \times 10$$^{10}$$\ \mathrm{Pa}$$

Q: Two musicians try to play the same note, which has a wavelength of 65 cm, at the same time. One instrument is out of tune and plays a note with a wavelength of 65.4 cm. What is the frequency of the beats the musicians hear? (Assume $$v = 343\ \mathrm{m/s})$$

$$f_{\text{beat}} = 2.7\ \mathrm{Hz}$$

Question 1

A sound wave travels through air at a speed of 343 m/s. What is the wavelength of a sound wave with a frequency of 260 Hz?

Accepted Answer

$$\lambda = \dfrac{343}{260} = 1.32\ \mathrm{m}$$

Question 2

A rope with length 2.50 m and mass 0.10 kg is stretched and pulled to create transverse waves of frequency 40.0 Hz and wavelength of 0.750 m. How much tension is exerted on the rope?

Accepted Answer

$$F_T = 6\ \mathrm{N}$$

Question 3

You and your friend hold a rope at both ends, and pull it taut with a tension of 30 N. The rope is 7.5 m long, and has a mass of 0.5 kg. How long does it take for a wave pulse to travel from you to your friend?

Accepted Answer

$$t = \dfrac{7.5}{\sqrt{30/ (0.5/7.5)}} = 1.12\ \mathrm{s}$$

Question 4

A metal bar has a length of 1.5 m and a density of $$6400\ \mathrm{kg/m^3$}. $$Sound waves take $$3.9 	imes 10$$^{-4}$$ s to travel along the length of the bar. What is the Young’s modulus for this metal?

Accepted Answer

$$Y = 9.47 	imes 10$$^{10}$$\ \mathrm{Pa}$$

Question 5

A sound source radiates sound waves in all directions. At a distance of 4 m from the source, you measure the wave intensity to be $$0.06\ \mathrm{W/m^2$}. $$How much sound energy does the source emit in 1 hour if the power output is constant?

Accepted Answer

$$E = 10,860\ \mathrm{J}$$

Question 6

You measure the intensity from a sound source to be $$0.3\ \mathrm{W/m^2$} at a $$distance of 3.4 m. What will the intensity be if you walk closer to the source, to a distance of 2.5 m?

Accepted Answer

$$I = 0.55\ \mathrm{W/m^2$}$$

Question 7

A sound wave from a police siren has an intensity of $$0.01\ \mathrm{W/m^2$} at a $$certain distance. A second sound wave from an ambulance has a sound intensity level 8 dB greater than the police siren, when measured at the same distance. What is the sound intensity level (in dB) of the sound wave due to the ambulance?

Accepted Answer

$$\beta = 108\ \mathrm{dB}$$

Question 8

A transverse harmonic wave moving to the left has a wavelength of 2.5 m and a wave speed of 12 m/s. The amplitude of the wave is 0.1 m. At $$x=0$$ and $$t=0$$, the displacement of the wave is $$y = 0. $$Write the wave function for this wave.

Accepted Answer

$$y(x, t) = 0.1 \sin(2.51x + 30.2t)$$

Question 9

A horizontal string is stretched with a tension of 90 N, and the speed of transverse waves for the wire is 400 m/s. What must the amplitude of a 70.0 Hz traveling wave be for the average power carried by the wave to be 0.365 W?

Accepted Answer

$$A = 2.9\ \mathrm{mm}$$

Question 10

A 3 m-long rope is stretched between two supports with a tension that makes the speed of transverse waves 60 m/s. What are the wavelength and frequency of the second overtone?

Accepted Answer

$$\lambda = 2\ \mathrm{m};\ f = 30\ \mathrm{Hz}$$

Question 11

The fundamental frequency of your closed organ pipe is 200 Hz. The second overtone of this pipe has the same frequency as the 3rd harmonic of an open pipe. What is the length of this open pipe? (Assume $$v = 343\ \mathrm{m/s})$$

Accepted Answer

$$L = 0.51\ \mathrm{m}$$

Question 12

Two musicians try to play the same note, which has a wavelength of 65 cm, at the same time. One instrument is out of tune and plays a note with a wavelength of 65.4 cm. What is the frequency of the beats the musicians hear? (Assume $$v = 343\ \mathrm{m/s})$$

Accepted Answer

$$f_{	ext{beat}} = 2.7\ \mathrm{Hz}$$

Question 13

A traveling transverse wave on a string can be modeled by the equation $$y(x, t) = 3 \cos (0.4x - 6t). $$What is the propagation velocity of the wave?

Accepted Answer

$$v = \dfrac{\omega}{k} = \dfrac{6}{0.4} = 15\ \mathrm{m/s}$$

Question 14

A string fixed at both ends is 8 m long and has a mass of 0.20 kg. It is subjected to a tension of 100.0 N and set oscillating. What is the longest possible wavelength for a standing wave?

Accepted Answer

$$\$$lambda_1$$ = 16\ \mathrm{m}$$

Question 15

A siren produces sound waves traveling radially outward. At a distance 15 m from the siren, the intensity of the wave is $$0.25\ \mathrm{W/m^2$}. At $$what distance will the intensity fall to $$0.01\ \mathrm{W/m^2$}$$?

Accepted Answer

$$r = 75\ \mathrm{m}$$

Question 16

A wave traveling to the right has an amplitude of 15 cm, wavelength of 40 cm, and oscillates 8 times per second. At $$t = 0$$, the displacement of a particle at $$x = 0$$ along this wave is $$+15 cm. $$Write the wave function, including the phase constant, using a sine function.

Accepted Answer

$$y(x, t) = 0.15 \sin(15.7x - 50.3t + 1.57)$$

Question 17

A standing wave on a wire is described by the wavefunction $$y(x, t) = [0.0025 \sin(0.75\pi x)] \sin(942 t). $$The left end of the wire is at $$x = 0. $$What is the distance between adjacent nodes?

Accepted Answer

$$\Delta x = \dfrac{\lambda}{2} = \dfrac{2\pi/0.75\pi}{2} = \dfrac{2}{0.75 	imes 2} = 0.67\ \mathrm{m}$$

Question 18

The alarm of a car at rest produces sound waves of frequency 550 Hz. You’re riding on a motorcycle, traveling directly towards it, and you hear an observed frequency of 600 Hz. How fast must you be traveling? (Assume $$v_{	ext{sound}} = 343\ \mathrm{m/s})$$

Accepted Answer

$$v_L = (\dfrac{f_L}{f_S} - 1) v = (\dfrac{600}{550} - 1) 	imes 343 = 31.2\ \mathrm{m/s}$$

Waves & Sound: Comprehensive Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards