- Which of the following combinations determines the wave speed (wave velocity)?
- Wavelength and phase angle
- Frequency and wavelength
- Phase angle and frequency
- Amplitude and frequency
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.
- 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?
- Lower pitch and shorter wavelength
- Lower pitch and longer wavelength
- Higher pitch and shorter wavelength
- Higher pitch and longer wavelength
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:
\(\lambda’ = \dfrac{v}{f’} < \dfrac{v}{f}\)
- As a sound wave travels through air, what is there a net transfer of?
- Energy only
- Mass only
- Mass and energy
- Neither mass nor energy
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.
- 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?
- Longitudinal
- Torsional
- Transverse
- Hyperbolic
In longitudinal waves, particle displacement is parallel to the direction of propagation. In transverse waves, displacement is perpendicular.
- 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?
- 10 Hz
- 2 Hz
- 20 Hz
- 40 Hz
One vibration spans one wavelength, so \(\lambda=2\text{ m}\).
Using \(v=f\lambda\):
\(f = \dfrac{v}{\lambda}=\dfrac{20}{2}=10\ \text{Hz}\)
- What is the period of a wave if 20 crests pass an observer in four seconds?
- 80 s
- 0.2 s
- 5 s
- 4 s
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:
\(T=\dfrac{t}{N}=\dfrac{4}{20}=0.2\ \text{s}\)
- 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?
- 0°
- 180°
- 90°
- 360°
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.
- As a pulse travels along a rope, the pulse loses energy. What happens to its amplitude?
- It decreases
- It increases
- It remains the same
For mechanical waves, the energy carried is proportional to the square of amplitude (\(E \propto A^2\)).
As energy dissipates, amplitude decreases.
- Compared to the wavelengths of visible light, the wavelengths of UV light are…
- Shorter
- Longer
- The same
Ultraviolet lies just beyond violet in the electromagnetic spectrum, with higher frequency and thus shorter wavelength than visible light:
\(\lambda_{\text{UV}} < \lambda_{\text{visible}}\)