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 degree celsius room is emitting a steady tone of 700 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 12 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? two significant figures, appropriate units

Explanation / Answer

wavelength = c / f = 343 m∙sâ » ¹ / 700 sâ » ¹ = 0.49 m

theta = arcsin( lameda/d )
= arcsin( 0.49 m / 1.2 m )
= 24.0999 °

tan( theta ) = y/x
=>
y = xtan(theta )
= 12 m * tan( 24.0999 ° )
=5.3677 m

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