A signal generator is connected to two loudspeakers L1 and L2, as shown in Fig. 2.1.

Question 9

A signal generator is connected to two loudspeakers L1 and L2, as shown in Fig. 2.1.

Fig. 2.1

A microphone M, connected to the Y-plates of a cathode-ray oscilloscope (c.r.o.), detects the intensity of sound along the line ABC.

The distances L1A and L2A are equal.

The time-base of the c.r.o. is switched off.

The traces on the c.r.o. when M is at A, then at B and then at C are shown on Fig. 2.2, Fig. 2.3 and Fig. 2.4 respectively.

                                   Fig. 2.2                                     Fig. 2.3                                      Fig. 2.4

For these traces, 1.0 cm represents 5.0 mV on the vertical scale.

(a) (i) Explain why coherent waves are produced by the loudspeakers. [1]

(ii) Use the principle of superposition to explain the traces shown with M at

1. A, [1]

2. B, [1]

3. C. [1]

(b) The sound emitted from L1 and L2 has frequency 500 Hz. The time-base on the c.r.o. is switched on.

The microphone M is placed at A.

On Fig. 2.5, draw the trace seen on the c.r.o.

On the vertical scale, 1.0 cm represents 5.0 mV. On the horizontal scale, 1.0 cm represents 0.10 ms.

Fig. 2.5

[3]

Reference: Past Exam Paper – November 2015 Paper 23 Q2

Solution:

(a) (i)

The loudspeakers are connected to the same signal generator.

(ii)

1.

{This is the central maxima.}

The waves (that overlap) have a phase difference of zero   OR a path difference

of zero and so

EITHER constructive interference occurs

OR the displacement is larger                                               

2.

{This is a minima.}

The waves (that overlap) have a phase difference of (n + ½) × 360° or (n + ½) × 2π rad      OR a path difference of (n + ½)λ and so

EITHER destructive interference occurs

OR the displacements cancel/smaller           

3.

{This is a maxima.}

The waves (that overlap) are in phase or have phase difference of n360° or 2πn rad       OR have a path difference of nλ and so

EITHER constructive interference occurs

OR the displacement is larger           

(b)

{Period = 1/f = 1/500 = 0.002 s = 2 ms}

time period = 0.002 s or 2 ms

{The scale is 1 cm represents 0.10 ms. So, we need 20 cm to represent a complete wave. The screen available is only 10 cm, so only half a wave will be displayed.}

wave drawn is half time period

amplitude 1.0 cm