Answer all probems step by step. Problems 2 A-C Assume that the speakers are in

Question

Answer all probems step by step. Problems 2 A-C

Assume that the speakers are in phase-that is they both emit a peak at the same time. What will I hear, constructive or destructive interference? Now I move the bottom speaker vertically. At what speaker separation will I hear the other type of interference from part (a)? Suppose I double the frequency of the speakers, what will I hear for the two separations in a) and b) above? Suppose I have two speakers, separated by 5.09 m, each emitting an 800 Hz sound and I listen at a point 30.0 m away as shown (not to scale). Use v = 343 m/s.

Explanation / Answer

a)

lamda = v/f = 343/800 = 0.429 m

r2 = sqrt(30*30 + 5.09*5.09) = 30.429 m

path difference = d = r2 - r1 = 30.429 - 30 = 0.429 m

==> path difference is equal to the wavelength, therefore the interference is constructive.

b)

for a distructive interference path difference must be lamda/2:

==> r2 - r1 = 0.429/2 = 0.214375 m

==> r2 - 30 = 0.214375

==> r2 = 30.214375 m

==> r2 = sqrt(30*30 + D*D)

==> 30.214375 = sqrt(30*30 + D^2)

==> D = 3.5928 m

==> D = 3.59 m

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