My question is from College Physics by serway/vuille 8th edition. The question i

Question

My question is from College Physics by serway/vuille 8th edition.

The question is...
A pair of speakers separated by 0.700 m are driven by the same oscillator at a frequency of 690 Hz. An observer originally positioned at one of the speakers begins to walk along a line perpendicular to the line joining the speakers.
(a) How far must the observer walk before reaching a relative maximum in intensity?
(b) How far will the observer be from the speaker when the first relative minimum is detected in the intensity?

Please show how to solve the problem as well as the answer.

Thank you.

Explanation / Answer

d = 0.700 m, f = 690 Hz. speed of sound v = 345 m/s, so = v/f = 0.5 m

find x

path difference = (d2 + x2) - x.

(a) a relative maximum in intensity

= ,

(d2 + x2) - x =

d2 + x2 = (x + )2

x = (d2 - 2)/(2) = 0.24 m

(b) the first relative minimum in the intensity

= /2,

(d2 + x2) - x = /2

d2 + x2 = (x + /2)2

x = (d2 - 2/4)/ = 0.86 m

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