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Question 16.10: THE SOUND OF SILENCE A directional loudspeaker directs a sou...

THE SOUND OF SILENCE

A directional loudspeaker directs a sound wave of wavelength λ at a wall (Fig. 16.14). At what distances from the wall could you stand and hear no sound at all?

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Your ear detects pressure variations in the air; you will therefore hear no sound if your ear is at a pressure node, which is a displacement antinode. The wall is at a displacement node; the distance from any node to an adjacent antinode is λ/4, and the distance from one antinode to the next is λ/2 (Fig. 16.14). Hence the displacement antinodes (pressure nodes), at which no sound will be heard, are at distances d = λ/4, d = λ/4 + λ/2 = 3λ/4, d = 3λ/4 + λ/2 = 5λ/4, c from the wall. If the loudspeaker is not highly directional, this effect is hard to notice because of reflections of sound waves from the floor, ceiling, and other walls.

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