At a concert two large speaker towers are right on the edge of a stage one at ea

Question

At a concert two large speaker towers are right on the edge of a stage one at each end 5.0 m apart. During a sound test, a pure tone of single frequency is played in phase from the speakers.

a)Person A is directly between the speakers 2.5 m from the edge of the stage. Person B is 2.5 m from the stage directly in front of the stage. If they both hear a maximally loud sound, what is the lowest possible frequency of the tone played?

b)A 243 Hz pure tone is now played. A worker stands on the edge of the stage directly between the speaker towers. She hears a maximally loud sound. How far must she walk towards a speaker to hear a minimally loud sound?

Explanation / Answer

Using interference of waves theory,

d=lambda/sin(theta); d is the distance between two maximum points or two minima...

Now, lambda = c/f; c= 343m/s....

For part A)

Given d = 2.5 m, with theta = 45

Lambda = c/f, f = 97 highters

For part B)

Given f = 243 hz... With theta 90 degrees

d = c/(fsin9)

d = 343/243

Now, diastance f is the gap between maxima and minima of the interference

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