Two speakers on a horizontal axis both emit #440# Hz sound waves. The two speakers are #pi# radians out of phase. If there is to be a maximum constructive interference what is the minimum separation distance between the two speakers?

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Mar 17, 2018

Answer:

0.39 meters

Explanation:

Because the two speakers are off by #pi# radians, they are off by half a cycle. To have maximum constructive interference, they must line up exactly, meaning one of them must be shifted over half a wavelength.

The equation #v=lambda*f# represents the relationship between frequency and wavelength. The speed of sound in air is approximately 343 m/s, so we can plug that into the equation to solve for #lambda#, the wavelength.

#343=440lambda#
#0.78=lambda#

Finally, we must divide the value of the wavelength by two because we want to shift them over half a cycle.

#0.78/2=0.39# meters, which is your final answer.

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