Sound (speed = 343 m/s) exits a diffraction horn Loudspeaker through a rectangul

Question

Sound (speed = 343 m/s) exits a diffraction horn Loudspeaker through a rectangular opening like a small doorway. A person is sitting at an angle theta off to the side of a diffraction horn that has a width D of 0.072 m. This individual does not hear a sound wave that has a frequency of 11000 Hz. When she is sitting at an angle of theta/2, the frequency that she does not hear is different. What is this frequency? Sound (speed = 343 m/s) exits a diffraction horn Loudspeaker through a rectangular opening like a small doorway. A person is sitting at an angle theta off to the side of a diffraction horn that has a width D of 0.072 m. This individual does not hear a sound wave that has a frequency of 11000 Hz. When she is sitting at an angle of theta/2, the frequency that she does not hear is different. What is this frequency?

Explanation / Answer

wavelength of sound wave, lamda = v/f

= 343/11000

= 0.03118 m

we know, condition for distructive interefrence, D*sin(theta) = m*lamda

for minimum angle m = 1

so, sin(theta) = lamda/D

= 0.03118/0.072

theta = sin^-1(0.03118/0.072)

= 25.6 degrees

in the second case, theta = 25.6/2

= 12.8 degrees

now use, sin(theta) = lamda/D

lamda = sin(theta)*D

= sin(12.8)*0.072

= 0.01595 m

so, f = v/lamda

= 343/0.01595

= 21502 hz <<<<<<<<---------------------Answer

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