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: A traveling transverse wave on a string is described by $$y(x, t) = 3 \cos(0.4x - 6t). $$What is the maximum transverse velocity of particles on the string?

$$v_{T, max} = A\omega = 3 \times 6 = 18\ \mathrm{m/s}$$

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 0.750 m. How much tension is exerted on the rope?

Accepted Answer

$$F_T = 36\ \mathrm{N}$$

Question 3

If the tension in a string is quadrupled, what happens to the speed of waves on the string?

Accepted Answer

The speed doubles: $$v_{new} = 2v_{old}$$

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 wave on a string is described by $$y(x, t) = 0.1 \sin(2.5x + 15.7t). $$What is the speed of this wave?

Accepted Answer

$$v = \dfrac{\omega}{k} = \dfrac{15.7}{2.5} = 6.28\ \mathrm{m/s}$$

Question 6

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 7

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

Accepted Answer

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

Question 8

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 9

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 speed of waves on the string?

Accepted Answer

$$v = \sqrt{\dfrac{F_T}{\mu}} = \sqrt{\dfrac{100}{0.025}} = 63.25\ \mathrm{m/s}$$

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 play notes with wavelengths of 65 cm and 65.4 cm, respectively. What is the beat frequency they hear? (Assume $$v = 343\ \mathrm{m/s})$$

Accepted Answer

$$f_{beat} = |f_1$ - f_2$| = |527.7 - 524.4| = 3.3\ \mathrm{Hz}$$

Question 13

A traveling transverse wave on a string is described by $$y(x, t) = 3 \cos(0.4x - 6t). $$What is the maximum transverse velocity of particles on the string?

Accepted Answer

$$v_{T, max} = A\omega = 3 	imes 6 = 18\ \mathrm{m/s}$$

Question 14

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? ($$\mu is $$not given, but use $$P_{avg} = \frac{1}{2}\mu \$$omega^2$$ A^2$ v)$$

Accepted Answer

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

Question 15

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 16

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

$$r_2$$ = $$r_1$$ \sqrt{\dfrac{$$I_1$$}{$$I_2$$}} = 15 \sqrt{\dfrac{0.25}{0.01}} = 75\ \mathrm{m}$$

Question 17

A wave pulse travels along a 7.5 m rope with a mass of 0.5 kg and tension of 30 N. How long does it take for the pulse to travel from one end to the other?

Accepted Answer

$$t = \dfrac{L}{v} = \dfrac{7.5}{\sqrt{30/0.0667}} = 0.75\ \mathrm{s}$$

Question 18

A closed organ pipe has a fundamental frequency of 200 Hz. What is the frequency of its second overtone?

Accepted Answer

$$f_5 = 5$$ 	imes 200 = 1000\ \mathrm{Hz}$$

Question 19

A car alarm emits a sound at 550 Hz. You are riding a motorcycle directly toward the car and hear a frequency of 600 Hz. What is your speed? (Assume $$v_{sound} = 343\ \mathrm{m/s})$$

Accepted Answer

$$v_L = v_{sound} \left( \dfrac{f_L}{f_S} - 1 \right) = 343 \left( \dfrac{600}{550} - 1 \right) = 31.2\ \mathrm{m/s}$$

Waves & Sound: Comprehensive Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard