The diagram shows two identical loudspeakers driven in phase by a common audio-frequency source.

Question 29

The diagram shows two identical loudspeakers driven in phase by a common audio-frequency source.

When a student moves along line XY, she notices that there are variations in the loudness of the sound. The regions in which the sound is heard are alternately loud and quiet as indicated on the diagram.

How may the distance between loud regions be reduced?

A decreasing the distance a between the speakers

B increasing distance d

C increasing the frequency of the audio-frequency source

D increasing the power output from the audio-frequency source

Reference: Past Exam Paper – November 2012 Paper 12 Q28

Solution:

Answer: C.

The two loudspeakers produce sound wave that are in phase since the loudspeakers are identical. So, this question involves 2-source interference with sound waves.

A loud sound is heard due to constructive interference while a quiet sound is due to destructive interference.

Fringe separation x = λd / a

The fringe separation x gives the distance between loud regions.

Decreasing the distance a between the speakers causes the fringe separation to increase.

Increasing d also increases the fringe separation x.

Increasing the frequency of the audio-frequency source causes the wavelength λ to decrease (since v = f λ). Thus, this causes the fringe separation x to decrease. [C is correct]

Increasing the power output from the audio-frequency source causes the intensity, and thus the amplitude, of the wave to increase. This does not affect the fringe separation. The loud sound becomes louder.