SAT Physics Subject Test

Chapter 13 Waves

Chapter 13 Review Questions

See Chapter 17 for solutions.

  1. What is the wavelength of a 5 Hz wave that travels with a speed of 10 m/s ?

(A) 0.25 m

(B) 0.5 m

(C)   1 m

(D)   2 m

(E) 50 m

  2. A rope of length 5 m is stretched to a tension of 80 N. If its mass is 1 kg, at what speed would a 10 Hz transverse wave travel down the string?

(A)   2 m/s

(B)   5 m/s

(C)  20 m/s

(D)  50 m/s

(E) 200 m/s

  3. A transverse wave on a long horizontal rope with a wavelength of 8 m travels at 2 m/s. At t = 0, a particular point on the rope has a vertical displacement of +A, where A is the amplitude of the wave. At what time will the vertical displacement of this same point on the rope be –A ?

(A) t =  s

(B) t =  s

(C) t =  s

(D) t = 2 s

(E) t = 4 s

  4. What is the wavelength of a wave with period 2 s and speed 2 cm/s ?

(A) 0.25 cm

(B) 0.5 cm

(C) 1 cm

(D) 2 cm

(E) 4 cm

  5. A string, fixed at both ends, supports a standing wave with a total of 4 nodes. If the length of the string is 6 m, what is the wavelength of the wave?

(A) 0.67 m

(B) 1.2 m

(C) 1.5 m

(D) 3 m

(E) 4 m

  6. A string, fixed at both ends, has a length of 6 m and supports a standing wave with a total of 4 nodes. If a transverse wave can travel at 40 m/s down the rope, what is the frequency of this standing wave?

(A)  6.7 Hz

(B) 10.0 Hz

(C) 13.3 Hz

(D) 20.0 Hz

(E) 26.7 Hz

  7. A sound wave travels through a metal rod with wavelength λ and frequency f. Which of the following best describes the wave when it passes into the surrounding air?





Less than λ

   Equal to f


Less than λ

   Less than f


Greater than λ

   Equal to f


Greater than λ

   Less than f


Greater than λ

   Greater than f

  8. In the figure below, two speakers, S1 and S2, emit sound waves of wavelength 2 m, in phase with each other.

Let AP be the amplitude of the resulting wave at point P, and AQ the amplitude of the resultant wave at point Q. How does AP compare to AQ ?

(A) Ap < AQ

(B) Ap = AQ

(C) Ap > AQ

(D) Ap < 0, AQ > 0

(E) Ap and AQ vary with time, so no comparison can be made.

  9. An observer is 2 m from a source of sound waves. By how much will the sound level decrease if the observer moves to a distance of 20 m ?

(A)   1 dB

(B)   2 dB

(C) 10 dB

(D) 18 dB

(E) 20 dB

10. An organ pipe that’s closed at one end has a length of 17 cm. If the speed of sound through the air inside is 340 m/s, what is the pipe’s fundamental frequency?

(A)    250 Hz

(B)    500 Hz

(C) 1,000 Hz

(D) 1,500 Hz

(E) 2,000 Hz

11. A bat emits a 40 kHz “chirp” with a wavelength of 8.75 mm toward a tree and receives an echo 0.4 s later. How far is the bat from the tree?

(A)   35 m

(B)   70 m

(C) 105 m

(D) 140 m

(E) 175 m

12. A car is traveling at 20 m/s away from a stationary observer. If the car’s horn emits a frequency of 600 Hz, what frequency will the observer hear? (Use v = 340 m/s for the speed of sound.)

(A) (34/36)(600 Hz)

(B) (34/32)(600 Hz)

(C) (36/34)(600 Hz)

(D) (32/34)(600 Hz)

(E) (32/36)(600 Hz)


mechanical wave

traveling wave












constructive interference

destructive interference

in phase

out of phase

standing wave



harmonic (resonant) wavelengths

harmonic number

harmonic (resonant) frequencies

fundamental standing wave




bulk modulus



Doppler effect



decibel level


·        For traveling waves, in which the peaks and valleys visibly move along the length of a rope, the displacement y of each point depends also on x and t.

·        In the point of view in which x varies, and t does not, we “freeze time” and see the-points at which the wave crosses the horizontal, the maximum vertical displacement above the horizontal (crests), and the maximum vertical displacement below the horizontal (the troughs).

·        In the point of view in which t varies, and x does not, you designate one position x along the rope to watch as time varies. The point on the rope will oscillate vertically and the wave propagates, or travels, horizontally.

·        The five most important characteristics of a traveling wave are its wavelength, amplitude, period, frequency, and speed.

·        The equation to determine wave speed on a stretched string is v = .

·        Superposition of waves is the concept that when two or more waves meet, the displacement at any point of the medium is equal to the sum of the displacements due to the individual waves. When waves meet and overlap (interfere) the displacement of the string is equal to the sum of the individual displacements.

·        Constructive interference creates a combined wave of greater magnitude than either individual wave. Destructive interference results in a combined waveform that has a displacement of a smaller magnitude that either individual wave.

·        Standing waves are seen when two oppositely traveling waves that have the same frequency, amplitude, and wavelength oscillate vertically and remain fixed. The crests and troughs do not appear to travel down the length of the string.

·        Sound waves are produced by the vibration of an object. The vibrations cause pressure variations in the conducting medium: Compressions are where the molecules are bunched together (the pressure is above normal). Rarefactions are the positions where the pressure is below normal.

·        Sound waves differ from waves on strings in that the molecules of a medium transmitting a sound wave move parallel to the direction of wave propagation rather than perpendicular to it.

·        Intensity and decibel level measure the loudness of a sound. Decibel level is measured on a logarithmic scale.

·        Resonance for sound waves follows a pattern of nodes and anti-nodes. While an open-ended tube can support any harmonic—any integer times –λ, a closed-end tube can only support odd harmonics—an odd multiple of λ.

·        The Doppler effect occurs when there is relative motion between the source of the sound waves and the detector. When the detector moves toward the source (or vice-versa), he or she intercepts the waves at a rate higher than the one at which they were emitted and hears a higher frequency than the source emitted. If the detector is moving away from the source or if the source is moving away from the detector, the detected waves have a lower frequency than originally emitted by the source.

·        Light, or electromagnetic waves, also experiences the Doppler effect. Motion toward the source corresponds to a frequency shift upward (and a wavelength shift downward). Motion away from the source corresponds to a frequency shift downward (and a wavelength shift upward).