Two loud speakers, each receiving the same signal of frequency 6.800 kHz from an

Question

Two loud speakers, each receiving the same signal of frequency 6.800 kHz from an amplifier, and thereforeoscillating in phase with each other, are arranged as shown in the diagram below. A microphone M can be moved up anddown the line AB. Use v = 340.0 m/s as the speed of sound. Note that the diagram is NOT to scale.

The microphone M is moved from O alone the line AB. Maxima and minima in the detected sound intensity are detected.

(i) What is the distance between adjacent maxima?

(ii) What is the distance between adjacent minima

Explanation / Answer

for mth maxima ,distancefrom the central line ig given by

ym =mD/d where D=distance of loudspeaker from line AB,d=distance btw the loudspeakers

ym+1 =(m+1)D/d

since v=f* =>=v/f=340/6800

distance btw adjacent maxima=D/d=(34/680)*(200/2)=5 m

fornth minima ,distancefrom the central line ig given by

yn=(2n+1)D/2d

distance btw adjacent minima =yn+1-yn =D/d =5m

hence the distance btw adjacent maxima is 5m

& the distance btw adjacent minima is 5m

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