Two speakers, separated by a distance x = 5.37 m are driven in phase by the same

Question

Two speakers, separated by a distance x = 5.37 m are driven in phase by the same amplifier. A listener is located at point A, a distance L = 2.62 m directly in front of one of the speakers.

1) What is the lowest frequency for which there is a maximum signal at A due to constructive interference? The speed of sound can be taken as 3.43 × 102 ms.

2) What is the second lowest frequency for which there is a maximum signal?

3) What is the lowest frequency for which there is a minimum signal due to destructive interference?

4) What is the second lowest frequency for which there is a minimum signal?

Explanation / Answer

given data
distance x=5.37m
L = 2.62 m
v=3.43*10^2m/s

What is the longest wavelength for which there is a maximum signal at A due to constructive interference?

Path difference = sq rt[2.62^2 + 5.37^2] - 2.62= 3.355 m
That is the longest wavelength for which there will be constructive interference.

What is the lowest frequency for which there is a maximum signal at A due to constructive interference?
lowest frequency = 343/3.355 = 102.23 Hz  

What is the second lowest frequency for which there is a maximum signal?
102.23*2 =204.47 Hz

What is the lowest frequency for which there is a minimum signal due to destructive interference?
lambda/2 = 3.355

lambda = 6.71

Coresponding frequency = 343/6.71= 51.1 Hz

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