Question

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Microphone - - - - Speakers Click to go forward, hold to see history Two small speakers are separated by a distance of 6 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 14 m away from the speakers on the axis running through the middle of the two 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 as measured from the axis? The speed of sound in air is 343 m/s. Do not use the small angle approximation for this problem. 0.118 0.118 NO m (from axis) Enter Help Try again. Click on the Help button if you are having trouble with this problem.

Answer 1

Frequency = 14kHz = 14000 Hz

wavelength of the signal will then be: $\lambda = \frac{c}{f} = 0.0245 m$

For 1st order minima,

$d\frac{x}{L} = \frac{\lambda}{2}$

$0.06\frac{x}{1.4} = \frac{0.0245}{2}$

=> x = 0.286m

this is the distance from the center where the first minima occurs.