Two loud speakers in a 20 o C room emit 686 Hz soundwaves along the x-axis. What

Question

Two loud speakers in a 20oC room emit 686 Hz soundwaves along the x-axis. What is the smallest distance between thespeakers for which the interference of the sound waves isdestructive? Can someone please help me out with this question at hand?THANKSSSS!!! All the best! Two loud speakers in a 20oC room emit 686 Hz soundwaves along the x-axis. What is the smallest distance between thespeakers for which the interference of the sound waves isdestructive? Can someone please help me out with this question at hand?THANKSSSS!!! All the best!

Explanation / Answer

First, you need to find the wavelength of the sound wave. Dothis by using the equation = v / f, where is thewavelength, v is the speed of sound in air at 20 degrees Celsius(343 m/s), and f is the frequency of the wave (686 Hz). = v / f = 343 / 686 = 0.5 meters Now, destructive interference will occur when the waves are off by radians, because then every peak on one wave will becanceled out by a trough from the other wave. So, the wavesneed to differ in phase by radians. radians ishalf of the complete phase, so the waves will differ in phase byhalf of the wavelength. Since the wavelength is 0.5 meters, destructive interference willoccur when the speakers are 0.25 meters apart. This process is fairly simple because the two speakers are on thesame line with respect to the interference point. Some basictrig is needed when the two speakers and interference point form atriangle, but that's not in this problem.

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