Question

Given figure shows a sound filter in which sound is passing through a bifurcated pipe. Speed of sound in air is $300\text{m/sec}$. A sound consists of four frequencies $300\text{Hz},600\text{Hz},900\text{Hz},1500\text{Hz}$.
Then which of the following frequency will pass through outles

• A. $300\text{Hz}$
• B. $600\text{Hz}$
• C. $900\text{Hz}$
• D. $1500\text{Hz}$

Answer 1

The correct option is B $600\text{Hz}$

The frequency of sound waves, for which destructive interference occurs will result into a net zero intensity of resultant sound. Hence these waves will not pass through filter.
Condition for destructive interference (Minimum Intensity),
$\Rightarrow \Delta x=(2n+1)\frac{\lambda }{2}...\left(i\right)$
The path difference between waves arriving through two routes of the bifurcated pipe is,
$\Delta x=x_2-x_1$
$\Rightarrow \Delta x=(25+25+25)\text{cm}-25\text{cm}$
$\therefore \Delta x=50\text{cm}=0.5\text{m}$
From Eq. ($i$),
$(0.5\times 2)=(2n+1)\lambda$
$\Rightarrow 1=(2n+1)\frac{V}{f}$
$\Rightarrow f=(2n+1)V=(2n+1)300$
For ($n=0,1,2,$... etc) we get:
$f=300\text{Hz},900\text{Hz},1500\text{Hz}$,...etc
Hence odd multiples of $300\text{Hz}$ will not pass through filter.