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In Fig. 17 - 45, a sound of wavelength 0.750 m is emitted isotropically by point

ID: 1991468 • Letter: I

Question

In Fig. 17 - 45, a sound of wavelength 0.750 m is emitted isotropically by point source S. Sound ray 1 extends directly to detector D, at distance L = 11.3 m. Sound ray 2 extends to D via a reflection (effectively a bouncing) of the sound at a flat surface. The reflection occurs on a perpendicular bisector to the SD line, at distance d from the line. Assume that the reflection shifts the sound wave by 0.500lambda. For what least value of d (other than zero) do the direct sound and the reflected sound arrive at D (a) exactly out of phase and (b) exactly in phase?

Explanation / Answer

(11.32 + 4d2) - 11.3 = 0.75 m

127.69 + 4d2 = 145.2025

4d2 = 17.5125

d2 = 4.378

d = 2.092 m

(11.32 + 4d2) - 11.3 = 0.75/2 m

127.69 + 4d2 = 136.3056

4d2 = 8.616

d2 = 2.154

d = 1.468 m