Question #162542

Sound with a frequency of 650Hz from a distant source passes through a doorway. 1.10m wide in a sound absorbing wall. Find

(a) the number and (b) the angular directions of the diffraction minima at listening positions along a line parallel to the wall.


1
Expert's answer
2021-03-01T07:21:34-0500

Answer

Wavelength

λ=vsf=343650=0.528m\lambda=\frac{v_s}{f}=\frac{343}{650}=0.528m

Conditions for diffraction minima

asinθ=mλasin\theta=m\lambda

Where

m=±1,±2,±3,.....m=\pm1 ,\pm2 ,\pm3,.....

Now

θ1=sin1(±10.5281.1)=±28.7°\theta_1=\sin^{-1}(\pm1\frac{0.528}{1.1}) =\pm28.7^°


θ2=sin1(±20.5281.1)=±73.7°\theta_2=\sin^{-1}(\pm2\frac{0.528}{1.1}) =\pm73.7^°



θ3=sin1(±30.5281.1)=\theta_3=\sin^{-1}(\pm3\frac{0.528}{1.1}) = non-exist


Therefore

a) four minima

b) angular directions are

±28.7°,±73.7°.\pm28.7^°, \pm73.7^°.


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