Sound waves of frequency 530 Hz enter a window 1.16 m wide. The window is in the

Question

Sound waves of frequency 530 Hz enter a window 1.16 m wide. The window is in the exact center of one wall of a theater 24 m by 13 m. The window is 13 m from the opposite wall, along which is a row of seats occupied by people. The theater is acoustically prepared to prevent the reflection of sound waves, and the speed of sound is 330 m/s. Two people, on each side of a line directly in front of the window, in the row along the wall hear no sound.
What minimum distance are they from each other? The angle may be too large to use small angle approximation.
Answer in units of m.

Explanation / Answer

soundwaves of the frequency is f = 530 Hz    wide of the window is d = 1.16m , L = 13.0m    wavelength is = v / f                              = 330 m/s / 530 Hz                             = 0.622m                       sin = / d ........(1)                x / L = tan .......(2) From the above two equations      x = L tan ( sin^-1 ( / d ) )         = 13.0m tan ( sin^-1 ( 0.622m / 1.16m ) )         = 8.25m minimum distance are they from each other is   x = 2 * 8.25 m                                                                            = 16.5 m

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