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147.

Problem 20.31 (RHK)

Two stereo loud speakers are separated by a distance of 2.12 m. We may assume that the amplitude of the sound from each speaker is approximately the same at the position of a listener, who is 3.75 m directly in front of one of the speakers. We have to find (a) the frequencies in the audible range (20 - 20,000 Hz) for which there will be a minimum signal; (b) the frequencies for which there will be a maximum signal.

Solution:             Click For PDF Version

The stereo speakers are separated as shown in the figure. It is assumed that the amplitude of the sound from each speaker is approximately the same at the position of the listener, who is 3.75 m directly in front of one of the speakers.

The distance from the second speaker to the listener is

The distance from the first speaker to the listener is

The condition for minimum at the position of the listener is

Frequencies that will produce a minimum will therefore be

As,

frequencies in the audible range that will produce a minimum are

The condition for maximum at the position of the listener is

As,

frequencies in the audible range that will produce a maximum are