Question

Sound signal is sent through a composite tube as shown in the Figure 14.24. The radius of the semicircular portion of the tube is $r$. The speed of sound in air is $v$. The source of sound is capable of giving sound of varied frequency. If $n$ is an integer then frequency for maximum intensity is given by:

• A. $nv/r$
• B. $nv/r(\pi -2)$
• C. $nv/\pi r$
• D. $nv/\pi (r-2)$

Answer 1

The correct option is B $nv/r(\pi -2)$

Path difference between the waves reaching the point B $\Delta x=\pi r-2r$

$\Delta x=(\pi -2)r$

Let frequency of the sound wave be $\nu$

If maximum intensity is obtained at B, then $\Delta x=n\lambda$ where $\lambda$ is the wavelength of sound

Thus $(\pi -2)r=n\frac{v}{\nu }$ $⟹\nu =\frac{nv}{(\pi -2)r}$