Question

In a Quincke's tube experiment, there is no change in sound intensity being detected at an appropriate point, when the slidable tube is drawn out by $x\text{cm}.$ If the speed of sound in air is $340\text{m/s}$ and frequency of this sounding source is $1700\text{Hz}$, then the value of $x$ is

Answer 1

Given that, velocity of sound $\left(v\right)=340\text{m/s}$
frequency of source $\left(f\right)=1700\text{Hz}$

Sliding tube is pulled out by distance of $x\text{cm}$ , this introduces a path difference of $2x\text{cm}$

Since there is no change in intensity when the tube moves by distance $x\text{cm}$
Path difference is $\lambda$

$\therefore 2x=\lambda$

But , $\lambda =\frac{v}{f}\Rightarrow 2x=\frac{v}{f}$
Substituting the data given in the question,

$x=\frac{340\times 100}{2\times 1700}=10\text{cm}$