Two loudspeakers in a plane are 2.0 m and in phase with each other. Both emit 70

Question

Two loudspeakers in a plane are 2.0 m and in phase with each other. Both emit 700 Hz sound waves into a room where the speed of sound is 341 m/s. A listener stands 5.0 m in front of the loudspeakers and 2.0 m to one side of the center.(You will have to explain all your answers/method in brief). Find the wave length of the sound waves. (3)Find r_1, r_2, delta r, delta phi (9) Is the interferences at this point a maximum constructive, perfect destructive or in between?(4) How will the situation differ if the loudspeakers are out of phase to begin with? What kind of interference do you see at the point that is 5 m away from the center of the line joining the speakers and equidistant from the speakers are in the case when the speakers are in the phase and out of phase?

Explanation / Answer

A) wavelength = 341/700 = 0.487 m

B) r1 = sqrt(52 +12) = 5.099 m,

  r2 = sqrt(52 + 32) = 5.831 m

dr = 5.831 - 5.099 = 0.732 m

C) 0.732 / 0.487 = 1.5

so path difference is 1.5 times the wavelength so interference is destructive.

D) then the constructive interference will be there.

E) as path difference = 0

for out of phase conditions, destructive interference

for into phase conditions, constructive interference

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