Two speakers, which are separated by a distance d = 3.00 m, produce sound waves

Question

Two speakers, which are separated by a distance d = 3.00 m, produce sound waves with the same amplitude, phase and frequency. You stand a distance of 1.50 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

d= 3 m , h =1.5m

for constructive interference

DL = m(lamda) , for m=1

DL = lamda = (h^2+d^2)^0.5 - h

lamda = (3^2 +1.5^2)^0.5 -1.5 =1.854 m

velocity of sound in air v = 340 m/s

v =f*lamda

340 = f*1.854

f = 183.4 Hz

(b) for destructive interference

DL = (lamda)/2 = (h^2+d^2)^0.5 - h

lamda/2 = (3^2 +1.5^2)^0.5 -1.5 =1.854 m

lamda = 3.708 m

f = v/lamda = 340/3.708 =91.7 Hz

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