Question

In a Quincke's tube experiment, when the sliding tube is pulled out by $17\text{mm}$, the intensity of sound varies from minimum to maximum value. Find the frequency of sound source, if the speed of sound in air is $340\text{m/s}$.

• A. $1\text{kHz}$
• B. $2\text{kHz}$
• C. $5\text{kHz}$
• D. $10\text{kHz}$

Answer 1

The correct option is C $5\text{kHz}$

Given that,
Velocity of sound $\left(v\right)=340\text{m/s}$

Distance moved by the sliding tube $\left(x\right)=17\text{mm}$

When the sliding tube moves by a distance $x$, path difference effected is $2x$.

When intensity varies from minimum to maximum value, path difference is increased by $\frac{\lambda }{2}$
$\therefore 2x=\frac{\lambda }{2}\Rightarrow x=\frac{\lambda }{4}$
But, $\lambda =\frac{v}{f}\therefore f=\frac{v}{4x}$

Substituting the given data, we get

$f=\frac{340}{4\times 17\times {10}^{-3}}=5000\text{Hz}\text{or}5\text{kHz}$