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?

vrteclh

vrteclh

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2022-08-16

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

Answer & Explanation

Hamza Conrad

Hamza Conrad

Beginner2022-08-17Added 20 answers

Because the two speakers are off by π 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 = λ 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 λ , the wavelength.
343 = 440 λ
0.78 = λ
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 m e t e r s

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