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}$$\ \mathrm{Pa}$$

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

$$\lambda = 1.32\ \mathrm{m}$$

Question 2

A wave has a wavelength of 10 mm and moves at a speed of 50 mm/s. What is the frequency of this wave?

Accepted Answer

$$f = 5\ \mathrm{Hz}$$

Question 3

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 4

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

Accepted Answer

The wave speed doubles.

Question 5

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 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 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 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 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 10

By whipping a string up and down, you determine the fundamental frequency to be 4 Hz. If you attach the string to a motorized oscillator and increase the frequency to 28 Hz, how many loops would this standing wave have?

Accepted Answer

7

Question 11

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

$$v = 20\ \mathrm{m/s}$$

Question 12

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 13

Which of the following best describes the principle of superposition for waves?

Accepted Answer

The net displacement at any point is the sum of the displacements due to each wave at that point.

Question 14

If two pulses of equal amplitude but opposite sign meet at a point on a string, what is the amplitude of the resultant wave at that point?

Accepted Answer

Zero

Question 15

A standing wave on a string is described by $$y(x, t) = (0.0025 \sin(0.75\pi x)) \sin(942 t). $$What is the distance between adjacent nodes?

Accepted Answer

$$\Delta x = \dfrac{2}{0.75} = 2.67\ \mathrm{m}$$

Question 16

Which of the following changes will NOT affect the speed of a wave on a string?

Accepted Answer

Doubling the frequency of the oscillator

Question 17

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

Accepted Answer

$$v_{T,\mathrm{max}} = 18\ \mathrm{m/s}$$

Wave Motion – Comprehensive Study Notes (Giancoli Ch. 15)

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