Answer to Question #164083 in Optics for Collins

Question

In a location where the speed of sound in air is 354ms^-1, a 200Hz sound wave impinges on two slits 30.0cm apart.

           a.) At what angle is the first maximum located?

           b.) If the sound is replaced by a 3.00cm microwave, what slit separation gives the same angle for the first maximum?

Answer 1

Answer

(A)

$\lambda=\frac{v}{f}$

$\lambda=\frac{354}{200}=1.77m$

Angle can be obtain as

$\theta=sin^{-1}(\frac{m\lambda}{d})$

By putting value

$\theta=sin^{-1}(\frac{(1)(0.177)}{0.30})=36.1^°$

(B)

$d=\frac {m\lambda}{sin\theta}$

By putting value

$d=\frac {(1)(0.0300)}{sin(36.1)°}$

$d=0.0508m$