Two small stereo speakers A and B that are 1.40 m apart are sending out sound of

Question

Two small stereo speakers A and B that are 1.40 m apart are sending out sound of wavelength 34.7 cm in all directions and all in phase. A person at point P starts out equidistant from both speakers and walks (see (Figure 1) ) so that he is always 1.50 m from speaker B. Limit your solutions to the cases where x1.50m.

A) For what values of x will the sound this person hears be maximally reinforced?

Express your answers in decreasing order to three significant figures, separated by commas.

B) For what values of x will the sound this person hears be cancelled?

Express your answers in decreasing order to three significant figures, separated by commas.

Explanation / Answer

A) For maximum sound, x = n

=> 1.50 - x = n

=> x = 1.50 - n = 1.50 - 0.347n

Now, 1.50 - 0.347n 0

=> n 1.50/0.347 = 4.3

So, n can take the following values: 0, 1, 2, 3, 4

So, x = 1.50 m, 1.15 m, 0.806 m, 0.459 m, 0.112 m

B)For cancellation of sound, x = (n + 0.5)

=> 1.50 - x = (n + 0.5)

=> x = 1.50 - (n + 0.5) = 1.50 - 0.347(n + 0.5)

Now, 1.50 - 0.347(n + 0.5) 0

=> n (1.50/0.347) - 0.5 = 3.8

So, n can take the following values: 0, 1, 2, 3

So, x = 1.33 m, 0.980 m, 0.632 m, 0.286 m

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