show all steps. and formulas used! In the figure, sound of wavelength 0.850 m es

Question

show all steps. and formulas used!

In the figure, sound of wavelength 0.850 m es ernimed isotropically by point source S. Sound ray tends directly to detector D wt ex distance L 10,0 m. Sound ray 2 extends to D via a reflection of the sound at a flat surface. That reflection occurs on a perpendicular bisector to the SD line, distance d from the line. Assume that the reflection shifts the sound wave For what least value of d (other than zero) do the direct sound and the renected sound arrive at D exactly in phase? Ray 2 Ray 1

Explanation / Answer

distance travelled by ray1 = r1 = L

distance travelled by ray2 = r2 = 2*sqrt(d^2 + (L/2)^2)

path difference dr = r2 - r1

for waves to be in phase

dr = m*lamda

2*sqrt(d^2 + (L/2)^2) - L = m*lambda

2*sqrt(d^2+5^2) - 10 = m*0.85

for m = 1

2*sqrt(d^2+5^2) - 10 = 1*0.85

d = 2.1 m <<<-----answer

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