Two speakers, which are separated by a distance d2.00 m, produce sound waves wit

Question

Two speakers, which are separated by a distance d2.00 m, produce sound waves with the same amplitude, phase and frequency. You stand a distance of 5.00 m directly in front of the left speaker, on the dashed line shown in the diagram (a) Assume the speed of sound to be 340 m/s. What is the lowest frequency the sound can have to produce completely constructive interference at your location? Hz (b) What is the lowest frequency the sound can have to produce completely destructive interference at your location? Hz

Explanation / Answer

distance travelled by sound from left speaker to you r1 = 5 m

distance travelled by sound from right speaker to you r2 = sqrt(5^2+2^2) = 5.38 m

path difference between the sound waves arriving at you dr = r2 - r1 = 0.38

(a)

for complete constructove interference

path difference = m*lambda

m = 1 ,2, 3, 4.......

r2 - r1 = m*v/f

v = speed of sound = 340 m/s

f = frequency of wave

for m =1

0.385 = 1*340/f

frequency f = 883 Hz

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part B

for complete destrucitve interference

path difference = m*lambda/2 = m*v/2f

for m = 1

0.385 = 1*340/(2f)

f = 441 Hz

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