Answer to Question #162542 in Optics for Samychou

Question

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.

Answer 1

Answer

Wavelength

$\lambda=\frac{v_s}{f}=\frac{343}{650}=0.528m$

Conditions for diffraction minima

$asin\theta=m\lambda$

Where

$m=\pm1 ,\pm2 ,\pm3,.....$

Now

$\theta_1=\sin^{-1}(\pm1\frac{0.528}{1.1}) =\pm28.7^°$

$\theta_2=\sin^{-1}(\pm2\frac{0.528}{1.1}) =\pm73.7^°$

$\theta_3=\sin^{-1}(\pm3\frac{0.528}{1.1}) =$ non-exist

Therefore

a) four minima

b) angular directions are

$\pm28.7^°, \pm73.7^°.$