CAIE A-Level Physics AS 7.1 Progressive Waves Questions

Practise reading wave diagrams and traces, calculating amplitude, phase, frequency, wavelength and speed, and relating progressive-wave energy to intensity.

Exam points

interpret amplitude, phase, period, frequency and wavelength from wave descriptions, graphs or CRO measurements
derive and apply v = fλ to calculate wave speed, frequency or wavelength with consistent units
explain progressive-wave energy transfer and calculate intensity using power, area and amplitude relationships

Covered syllabus points

7.1.1—What is meant by wave motion as illustrated by vibration in ropes, springs 7.1.2—The terms displacement, amplitude, phase difference, period, frequency 7.1.3—The use of the time-base and y-gain of a cathode-ray oscilloscope (CRO) to 7.1.4—The definitions of speed, frequency and wavelength, the wave equation v = f 7.1.5—V = f λ 7.1.6—Energy is transferred by a progressive wave 7.1.7—Intensity = power/area and intensity ∝ (amplitude)2

[Maximum number: 5]

A progressive transverse wave travelling from left to right is shown at an instant in time in Fig. 4.1.

Fig. 4.1

R and T are points on the wave.

(a)

State the phase difference between the points R and T .
phase difference =

[ 1 ]

$270^{\circ}$

(b)

On Fig. 4.1, draw an arrow at point T to show the direction of movement of point T at the instant shown.

[ 1 ]

(c)

The horizontal distance between R and T is 0.62 cm , as shown in Fig. 4.2.

Fig. 4.2 (not to scale)

The speed of the wave is $0.27 \mathrm{~ms}^{-1}$ .
Calculate the frequency of the wave.
frequency = Hz

[ 3 ]

$v=f \lambda$

or
$v=\lambda / T \text { and } f=1 / T$ $\begin{aligned} \text { wavelength } =0.62 \times 10^{-2} \times(4 / 3) ( \left.=0.83 \times 10^{-2} \mathrm{~m}\right) \end{aligned}$ $\begin{aligned} f =0.27 /\left(0.83 \times 10^{-2}\right) =33 \mathrm{~Hz} \end{aligned}$

[Maximum number: 5]

(a)

A loudspeaker oscillates with frequency f to produce sound waves of wavelength $\lambda$ . The loudspeaker makes N oscillations in time t.

[ 3 ]

(i)

State expressions, in terms of some or all of the symbols $f, \lambda$ and N, for:
1. the distance moved by a wavefront in time t

distance =

2. time t.

\text { time } t=

[ 2 ]

1. $N \lambda$
2. N / f

(ii)

Use your answers in (i) to deduce the equation relating the speed v of the sound wave to f and $\lambda$ .

[ 1 ]

v(= distance / time $)=N \lambda /(N / f)$ so $v=f \lambda$

(b)

The waveform of a sound wave is displayed on the screen of a cathode-ray oscilloscope (c.r.o.), as shown in Fig. 5.1.

Fig. 5.1

The time-base setting is $0.20 \mathrm{~ms} \mathrm{~cm}^{-1}$ .
Determine the frequency of the sound wave.

[ 2 ]

$T=4.0 \times 0.20=0.80(\mathrm{~ms})$ or $8.0 \times 10^{-4}(\mathrm{~s})$ $\begin{aligned} f =1 / 8.0 \times 10^{-4} =1300 \mathrm{~Hz} \end{aligned}$

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Covered syllabus points

Question 1

Question (a)

Question (b)

Question (c)

Question 2

Question (a)

Question (i)

Question (ii)

Question (b)