Question

A sound signal is sent through a composite tube as shown in the figure. The radius of the semicircular 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. $\frac{nv}{r}$
• B. $\frac{nv}{r(\pi -2)}$
• C. $\frac{nv}{\pi r}$
• D. $\frac{nv}{(r-2)\pi }$

Answer 1

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

The path difference between the waves moving along the straight path and semicircular path of composite tube,

$△x=\pi r-2r=(\pi -2)r$

For maxima this path difference be $n\lambda$

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

We have $\lambda =\frac{v}{f}$

Substituting the value of $\lambda$ in the above equation we get,

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

Frequency for maximum intensity

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