Q: A sinusoidal wave has a frequency $$f = 500 \ \mathrm{Hz}$$ and a wavelength $$\lambda = 0.68 \ \mathrm{m}. $$What is the speed of the wave?

$$v = f \lambda = 500 \times 0.68 = 340 \ \mathrm{m/s}$$

Q: A light wave travels from air (n = 1.0003) into glass (n = 1.50). If its wavelength in air is $$600 \ \mathrm{nm}$$, what is its wavelength in glass?

$$\lambda_{\text{glass}} = \frac{\lambda_{\text{air}}}{n_{\text{glass}}} = \frac{600}{1.50} = 400 \ \mathrm{nm}$$

Q: The intensity of a spherical sound wave at a distance $$r$$ from the source is given by:

$$I = \frac{P_{\text{source}}}{4\pi r^2$}$$

Question 1

Which of the following best describes a transverse wave?

Accepted Answer

A wave in which the displacement is perpendicular to the direction of travel.

Question 2

A string with a mass per unit length $$\mu = 0.005 \ \mathrm{kg/m} is $$stretched with a tension $$T = 20 \ \mathrm{N}. $$What is the speed of a wave on this string?

Accepted Answer

$$v = \sqrt{\frac{T}{\mu}} = \sqrt{\frac{20}{0.005}} = 63.2 \ \mathrm{m/s}$$

Question 3

Which of the following statements about sound waves is correct?

Accepted Answer

Sound waves are longitudinal waves and require a medium to propagate.

Question 4

A sinusoidal wave has a frequency $$f = 500 \ \mathrm{Hz}$$ and a wavelength $$\lambda = 0.68 \ \mathrm{m}. $$What is the speed of the wave?

Accepted Answer

$$v = f \lambda = 500 	imes 0.68 = 340 \ \mathrm{m/s}$$

Question 5

A light wave travels from air (n = 1.0003) into glass (n = 1.50). If its wavelength in air is $$600 \ \mathrm{nm}$$, what is its wavelength in glass?

Accepted Answer

$$\lambda_{	ext{glass}} = \frac{\lambda_{	ext{air}}}{n_{	ext{glass}}} = \frac{600}{1.50} = 400 \ \mathrm{nm}$$

Question 6

Which equation correctly gives the displacement $$D(x, t)$$ for a sinusoidal wave traveling in the positive x-direction?

Accepted Answer

$$D(x, t) = A \sin(kx - \omega t + \$$phi_0$$)$$

Question 7

A 100 Hz sound wave travels in air at $$343 \ \mathrm{m/s}. $$What is the phase difference between two points $$0.600 \ \mathrm{m}$$ apart?

Accepted Answer

$$\Delta \phi = 2\pi \frac{\Delta x}{\lambda} = 2\pi \frac{0.600}{3.43} = 1.10 \ \mathrm{rad}$$

Question 8

The intensity of a spherical sound wave at a distance $$r$$ from the source is given by:

Accepted Answer

$$I = \frac{P_{	ext{source}}}{4\pi r^2$}$$

Question 9

A police siren emits a frequency of $$f_0 = 500$$ \ \mathrm{Hz}$$. If the police car moves toward a stationary observer at v_s = 34.3$$ \ \mathrm{m/s}$$ and the speed of sound is v = 343$$ \ \mathrm{m/s}$$, what frequency does the observer hear?

Accepted Answer

$$f_+ = \frac{f_0$}{1 - v_s/v} = \frac{500}{1 - 34.3/343} = 550 \ \mathrm{Hz}$$

Question 10

A red laser pointer emits $$1.0 \ \mathrm{mW} of $$light into a $$1.0 \ \mathrm{mm}$$ diameter beam. What is the intensity of the beam?

Accepted Answer

$$I = \frac{P}{\pi r^2$} = \frac{0.0010}{\pi (0.0005)^2$} = 1300 \ \mathrm{W/m^2$}$$

Question 11

Which of the following is true about electromagnetic waves?

Accepted Answer

They can travel through a vacuum at speed $$c = 3.00 	imes 10^8$ \ \mathrm{m/s}.$$

Question 12

A sound wave in water has a bulk modulus $$B = 2.2 	imes 10^9$ \ \mathrm{Pa}$$ and density $$ho = 1000 \ \mathrm{kg/m^3$}. $$What is the speed of sound in water?

Accepted Answer

$$v_{	ext{sound}} = \sqrt{\frac{B}{ho}} = \sqrt{\frac{2.2 	imes 10^9$}{1000}} = 1483 \ \mathrm{m/s}$$

Question 13

The sound intensity level in decibels is given by:

Accepted Answer

$$\beta = 10 \log_{10} \left( \frac{I}{I_0$} \right)$$

Question 14

A galaxy emits light at $$656 \ \mathrm{nm} in $$the lab, but we observe it at $$691 \ \mathrm{nm}. $$What is the galaxy's speed relative to Earth?

Accepted Answer

$$v = c \frac{\lambda_{	ext{obs}} - \$$lambda_0$$}{\lambda_{	ext{obs}} + \$$lambda_0$$} = 3.00 	imes 10^8$ \frac{691 - 656}{691 + 656} = 1.56 	imes 10^7$ \ \mathrm{m/s}$$

Question 15

Which of the following best describes the Doppler effect for sound?

Accepted Answer

The frequency and wavelength of a sound wave are shifted if there is relative motion between source and observer.

Question 16

A wave pulse travels along a string at $$2.0 \ \mathrm{m/s}. If $$the leading edge of the pulse is $$4.0 \ \mathrm{m}$$ from a point, how long until the pulse reaches that point?

Accepted Answer

$$t = \frac{4.0}{2.0} = 2.0 \ \mathrm{s}$$

Traveling Waves: Physics with Calculus Study Notes

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