Wave Practice Problems

  1. Which of the following combinations determines the wave speed (wave velocity)?
  1. Wavelength and phase angle
  2. Frequency and wavelength
  3. Phase angle and frequency
  4. Amplitude and frequency
Show Answer
The correct answer is B!

Wave speed is given by \(v = f\lambda\) , the product of frequency \(f\) and wavelength \(\lambda\).

Equivalently, \(v=\tfrac{\omega}{k}\).

Phase angle and amplitude do not set the speed of a wave in a given medium.

 

  1. The driver of a car sounds a horn while traveling toward a stationary person. What characteristic does the sound heard by the stationary person have compared to the sound of the horn heard by the driver?
  1. Lower pitch and shorter wavelength
  2. Lower pitch and longer wavelength
  3. Higher pitch and shorter wavelength
  4. Higher pitch and longer wavelength
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The correct answer is C!

This is the Doppler effect. For a source moving toward a stationary observer, the observed frequency increases (with \(v_s > 0\) toward the observer):

\(f’ = \dfrac{v}{v – v_s}f\)

This means that the pitch is higher. The wavelength in front of the moving source is compressed, so it is shorter:

\(\lambda’ = \dfrac{v}{f’} < \dfrac{v}{f}\)

 

  1. As a sound wave travels through air, what is there a net transfer of?
  1. Energy only
  2. Mass only
  3. Mass and energy
  4. Neither mass nor energy
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The correct answer is A!

Mechanical waves in a medium transport energy without transporting matter overall. Air parcels oscillate about equilibrium (no net mass flow over a full cycle), but the disturbance carries energy forward.

 

  1. As a wave travels through a medium, the particles of the medium vibrate in the direction of the wave’s travel. What type of wave is traveling through the medium?
  1. Longitudinal
  2. Torsional
  3. Transverse
  4. Hyperbolic
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The correct answer is A!

In longitudinal waves, particle displacement is parallel to the direction of propagation. In transverse waves, displacement is perpendicular.

 

  1. A wave completes one vibration as it moves a distance of two meters at a speed of 20 meters per second. What is the frequency of the wave?
  1. 10 Hz
  2. 2 Hz
  3. 20 Hz
  4. 40 Hz
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The correct answer is A!

One vibration spans one wavelength, so \(\lambda=2\text{ m}\).

Using \(v=f\lambda\):

\(f = \dfrac{v}{\lambda}=\dfrac{20}{2}=10\ \text{Hz}\)

 

  1. What is the period of a wave if 20 crests pass an observer in four seconds?
  1. 80 s
  2. 0.2 s
  3. 5 s
  4. 4 s
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The correct answer is B!

Frequency is:

\(f = \dfrac{N}{t}=\dfrac{20}{4}=5\ \text{Hz}\)

Period is:

\(T=\dfrac{1}{f}=\dfrac{1}{5}=0.2\ \text{s}\)

Equivalently:

\(T=\dfrac{t}{N}=\dfrac{4}{20}=0.2\ \text{s}\)

 

  1. Two waves traveling in the same medium interfere to produce a standing wave. What is the phase difference between the two waves at a node?
  1. 0°
  2. 180°
  3. 90°
  4. 360°
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The correct answer is B!

At a node, displacement is always zero due to complete destructive interference, which requires the two contributing waves to be 180° (or \(\pi\) radians) out of phase. At antinodes they are in phase (0° or 360°) and reinforce.

 

  1. As a pulse travels along a rope, the pulse loses energy. What happens to its amplitude?
  1. It decreases
  2. It increases
  3. It remains the same
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The correct answer is A!

For mechanical waves, the energy carried is proportional to the square of amplitude (\(E \propto A^2\)).

As energy dissipates, amplitude decreases.

 

  1. Compared to the wavelengths of visible light, the wavelengths of UV light are…
  1. Shorter
  2. Longer
  3. The same
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The correct answer is A!

Ultraviolet lies just beyond violet in the electromagnetic spectrum, with higher frequency and thus shorter wavelength than visible light:

\(\lambda_{\text{UV}} < \lambda_{\text{visible}}\)