Question

A sound wave of wavelength 32 cm enters the tube as shown in the figure. Then the smallest radius $r$ so that a maximum of sound is heard at detector is :

• A. $7cm$
• B. $14cm$
• C. $21cm$
• D. $28cm$

Answer 1

The correct option is D $28cm$

For max sound two waves need to interfere constructively.
$\therefore$ Path difference for the waves has to be integer multiple of wavelength.
Path length $=S_1=\pi r$
Path length $=S_2=2r$
Path difference $=\Delta x=S_1-S_2=\pi r-2r=n\lambda$
For min radius$,n=1$
$\Rightarrow \pi r-2r=1\times \lambda$
$\Rightarrow r(\pi -2)=\lambda$
$\Rightarrow r\times 1.14=32$
$\Rightarrow r=\frac{32}{1.14}=28cm$