In Figure 12.5, two identical loudspeakers, A and B, driven by the same amplifie

Question

In Figure 12.5, two identical loudspeakers, A and B, driven by the same amplifier, are separated by 2.00 m and produce sound waves of the same frequency. Figure 12.5 A small microphone is placed at point C, 2.90 m from speaker A along the line perpendicular to the line connecting the two speakers. At this point destructive interference occurs. If the microphone is now moved along this line to point D, 5.00 m from speaker A, constructive interference occurs. Find the frequency of the sound waves. The speed of sound is 344 m/s. Assume that there are no other points between C and D where interference occurs.

Explanation / Answer

At C the path difference between the two arriving waves is v 2.8^2 + 2^2 – 2.8 = 0.641 m At D the pd is v4.1^2 + 2^2 – 4.1 = 0.462m the difference between these two pd's is ?/2 0.641 – 0.462 = ?/2 ? = 0.358 m F = 344 / 0.358 = 960 Hz

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