Two small speakers are separated by a distance of 7 cm, as shown. The speakers a

Question

Two small speakers are separated by a distance of 7 cm, as shown. The speakers are driven in phase with a sine wave signal of frequency 14 kHz. A small microphone is placed a distance 1m away from the speakers on the axis running through the middle of the 2 speakers, and the microphone is then moved perpendicular to the axis. Where does the microphone record the first minimum of the interference pattern from the speakers ad measured from the axis. The speed of sound in air is 343 m/s. Do not use small angle approx

Explanation / Answer

destructive interference condition is d*sin(theta) = (m+0.5)lamda

for first minimum m = 0

then d*sin(theta) = 0.5*lamda

theta = asin(0.5*lamda/d)

lamda = v/f = 343/14000 =0.0245 m

theta= asin(0.5*0.0245/0.07) = 10.07 degrees

ymin = L*tan(theta) = 1*tan(10.07) = 0.1777 m = 17.77 cm

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