Question

Sound signal is sent through a composite tube as shown in the figure. The radius of the semi-circular portion of the tube is r. Speed of sound in air is v. The source of sound is capable of giving varied frequencies in the range of $v_1$ and $v_2$ (where $v_2>v_1$). If n is an integer then frequency for maximum intensity is given by?

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

Answer 1

The correct option is A $\frac{nv}{f}$

the path difference between the wave is moving alone the straight path and semi circular path

$△x=\pi r=(\pi -2)r$

$(\pi -2)r=n\lambda$

$[\lambda =\frac{v}{f}]=(\pi -2)r=\frac{nv}{f}$