3.3.1.1 Progressive waves

Two points on a progressive wave have a phase difference of \frac{\pi }{6} rad.  The speed of the wave is 340 m s–1.

What is the frequency of the wave when the minimum distance between the two points is 0.12 m? 

• 240 Hz

• 470 Hz

• 1400 Hz

• 2800 Hz

A uniform wire, fixed at both ends, is plucked in the middle so that it vibrates at the first harmonic as shown.

What is the phase difference between the oscillations of the particles at P and Q?

• zero

• $\frac{\pi}{4}$ rad

• $\frac{\pi}{2}$ rad

• $\frac{\left(3\pi\right)}{4}$ rad

Which row shows the change in velocity, frequency and wavelength of an electromagnetic wave as it travels from an optically less dense to an optically more dense medium?

• A

• B

• C

• D

The graph shows how the vertical height of a travelling wave varies with distance along the path of the wave.

The speed of the wave is 20 cm s–1.

What is the period of the wave?

• 0.1 s

• 0.2 s

• 5.0 s

• 10.0 s

A progressive wave of frequency 150 Hz travels along a stretched string at a speed of 30 m s−1.

What is the phase difference between two points that are 50 mm apart on the string?

• zero

• 90°

• 180°

• 360°

For waves on a water surface, the following graph shows how the displacement y of a water particle in the surface varies with the time t.

What are the quantities z and s?

• z: frequency

  s: amplitude

• z: period

  s: half-amplitude

• z: wavelength

  s: half-amplitude

• z: period

  s: amplitude

Two coherent sources generate sound waves of wavelength 0.40 m. The waves leave the sources in phase. A detector some distance from the sources receives the sound waves. The path difference between the detector and the sources is 0.90 m.

What is the phase difference between the waves arriving at the detector?

• zero

• 45°

• 90°

• 180°

Two points on a progressive wave are one-eighth of a wavelength apart. The distance between them is 0.5 m, and the frequency of the oscillation is 10 Hz. What is the minimum speed of the wave?

• 0.2 m s^–1

• 10 m s^–1

• 20 m s^–1

• 40 m s^–1

Sound waves cross a boundary between two media X and Y. The frequency of the waves in X is 400 Hz. The speed of the waves in X is 330 m s^–1 and the speed of the waves in Y is 1320 m s^–1. What are the correct frequency and wavelength in Y?

• frequency/Hz: 100

  Wavelength (m): 0.82

• frequency/Hz: 400

  Wavelength (m): 0.82

• frequency/Hz: 400

  Wavelength (m): 3.3

• frequency/Hz: 1600

  Wavelength (m): 3.3

What is the phase difference between two points 0.16 m apart on a progressive sound wave of frequency 256 Hz?

speed of sound = 330 m s^–1

• $\frac{\pi}{8}$

• $\frac{\pi}{6}$

• $\frac{\pi}{4}$

• $\frac{\pi}{3}$