Sound and other waves undergo diffraction just as light does. Suppose a loudspea

Question

Sound and other waves undergo diffraction just as light does. Suppose a loudspeaker in a 20 degrees C room is emitting a steady tone of 1200 Hz. A 1.1-m-wide doorway in front of the speaker diffracts the sound wave. A person on the other side walks parallel to the wall in which the door is set, staying 16 m from the wall. When he is directly in front of the doorway, he can hear the sound clearly and loudly. As he continues walking, the sound intensity decreases.

- How far must he walk from the point where he was directly in front of the door until he reaches the first quiet spot?

Explanation / Answer

Minimum sound would be observed when
y = m * * D / a
where y = distance from central maximum
m = order of diffraction = 1 (for first minima)
= wavelength = v / f = 343 / 1200
= 0.285 m
D = distance between source and door = 16 m
a = width of door
y = 1 * 0.285 * 16 / 1.1
= 4.145 m
hence first quiet spot would be at 4.145 m.

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