Progressive Waves (CIE A Level Physics)

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]

Fig. 1.1 represents a progressive wave travelling from left to right on a stretched string.

Fig. 1.1

The frequency of the wave is 30 Hz. Calculate the speed of the wave.

State the phase difference between points X and Y on the string, giving an appropriate unit.

Describe how the vertical displacement of point X on the string varies in the next period.

Determine the phase difference between the current position of X and the position of X 0.0825 s later.

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:

Ultrasound is used to measure the depth of oceans, seas and lakes. 

Fig. 1.1 shows a pulse of ultrasound being emitted from the boat, travelling down to the sea bed and being reflected back to the boat.

Fig.1.1

State which type of wave ultrasound is and explain your answer.

A cathode-ray oscilloscope (C.R.O.) is used to trace the ultrasound pulses sent from the boat and the reflected pulses returning to the boat. The C.R.O. trace is shown in Fig. 1.2.

Fig. 1.2

The ultrasound travels through water at 1452 m s⁻¹, and the wavelength of the pulse is 0.023 m.

For the ultrasound pulses: 

The boat moves out to an area where the sea is deeper.