# 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

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 $v = \lambda \cdot f$ 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.

$343 = 440 \lambda$
$0.78 = \lambda$

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

$\frac{0.78}{2} = 0.39$ meters, which is your final answer.

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