Question

A sound signal is sent through a composite tube as shown in the figure. The radius of the semicircle is $R$ and speed of sound in air is $v$. If '$n$' is an integer, then the frequencies of the signal for obtaining maximum value of intensity are given by

• A. $\frac{nv}{R}$
• B. $\frac{nv}{(R-2)\pi }$
• C. $\frac{nv}{\pi R}$
• D. $\frac{nv}{R(\pi -2)}$

Answer 1

The correct option is D $\frac{nv}{R(\pi -2)}$

Since sound wave follows two different paths at the junction,
so, path difference $\Delta x=|\pi R-2R|$

and we know,
Path difference for maximum intensity $\Delta x=n\lambda [\lambda$ is the wavelength of wave]
$\therefore \pi R-2R=n\lambda$
As, $v=\lambda f$ we get,
$\pi R-2R=n\left(\frac{v}{f}\right)$
$\Rightarrow f=\frac{nv}{(\pi -2)R}$ are the frequencies for which maximum intensity is obtained.