Question

Sound signal is sent through a composite tube as shown in the figure. The radius of the semicircle is $r$. Speed of sound in air is $v$. The source of sound is capable to generate frequencies in the range $f_{1}to{f}_2(f_2>f_1)$. If $n$ is an integer then, frequency for maximum intensity is given by

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

Answer 1

The correct option is B $\frac{nv}{r(\pi -2)}$

For maximum intensity, path difference = $n\lambda$

Path difference in given case $=\pi r–2r$

$\Rightarrow n\lambda =\pi r–2r$

As $v=\lambda f$

$r(\pi –2)=\frac{nv}{f}$

Thus $f=\frac{nv}{r(\pi -2)}$