Loudspeaker Speaker
Mathematics: How far toward either speaker must the observer walk to first experience destructive interference?
Two loudspeakers are placed at either end of a gymnasium, both pointing toward the center of the gym and equidistant from it. The speakers emit 233-Hz sound that is in phase. An observer at the center of the gym experiences constructive interference. How far toward either speaker must the observer walk to first experience destructive interference?
First thing you need is the speed of sound, 340.29 m/s. We divide this by the frequency of the sound to find the wavelength 1.4604721 meters.
Now destructive interference will occur when the waves are 1/2 a length off, since he's standing at constructive interference the waves are exactly matched. Notice that if I travel 1/4 of a wave toward one speaker, I travel 1/4 of a wave away from the other speaker, this will yield the 1/2 wavelength difference that I need. Therefore he must travel 0.365 meters toward either speaker.
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