Reflection of sound

A form of sound-proofing is a fine wire mesh which is held at a fixed distance from a flat wall. When sound waves are normally incident on the wall, they first encounter the mesh. About half of the sound intensity is reflected, and half is transmitted. The transmitted sound waves can then travel the distance, \( d, \) reflect off the wall, travel the distance \(d\) again, and then combine with the original reflected sound from the wire mesh. If the two sound waves are exactly out of phase at this point, they will interfere destructively, reducing the total reflected sound intensity. If \( d = 2.54 \text{ cm} \) (one “inch”), what is the minimum frequency for which the sound-proofing will work properly?

The speed of sound is \( 343 \text{ m/s.} \)

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