Progressive Waves (CIE A Level Physics)

Fig. 1.1 shows a vertical cross-section through a water wave moving from left to right.

Fig. 1.1

Deduce the point at which the water is moving upwards at maximum speed and explain your reasoning. 

While a microphone is connected to a cathode-ray oscilloscope, a student strikes a tuning fork nearby. The sound wave produced by the tuning fork is displayed as a trace on the screen.

Fig. 1.2 shows the resulting trace. The time-base and gain are given on the screen.

Fig. 1.2

Use Fig. 1.2 to calculate the wavelength of the sound wave produced. 

(The speed of sound is approximately 330 m s^–1).

The student’s lab partner strikes another identical tuning fork near the microphone, so that both sound wave signals can be overlaid on the oscilloscope trace. Fig. 1.3 shows the new trace.

Fig. 1.3

Using Fig. 1.3, determine the phase difference between the two signals as shown on the oscilloscope trace. 

Give a suitable unit with your answer.

The oscilloscope trace is known as a ‘time-view’ of the sound wave because it shows the displacement of an oscillating signal against time. One of the students makes a time-view sketch as shown in Fig. 1.4, including a label M. 

An oscillating signal can also be shown in terms of a ‘space-view’, which would show the displacement of the signal against its position. The other student makes a space-view sketch as shown in Fig. 1.5, including a label N.

Fig. 1.4

Fig. 1.5

Show that the wave speed v is given by:

Circular water waves are produced by vibrating dippers at points P and Q, as illustrated in Fig. 4.1.

Fig. 4.1 (not to scale)

The waves from P alone have the same amplitude at point R as the waves from Q alone. Distance PR is 44 cm and distance QR is 29 cm.

The dippers vibrate in phase with a period of 1.5 s to produce waves of speed 4.0 cm s^–1.

wavelength = .................................................... cm [2]

path difference = ....................................................... λ [1]

[2]