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 deg C room is emitting a steady tone of 1200 Hz. A 1.2-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 18 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?
Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Frequency f = 1200 Hz Speed of light at 20 o C is v = 343 m / s Width of the door d = 1.2 m Wavelength = v / f                       = 0.2858 m Distance of the person from door D = 18 m Condition of first minimum intensity d sin =                                                  d ( y / D ) = From this y = D / d Subsitute values we get y = 4.2875 m

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