Question

A sound wave of frequency $600\text{Hz}$ falls normally on a perfect reflecting wall. The minimum distance from the wall at which the particles of the medium will have maximum displacement during their vibrations is
[speed of sound $=300\text{m/s}$]

• A. $\frac{7}{8}\text{m}$
• B. $\frac{3}{8}\text{m}$
• C. $\frac{1}{8}\text{m}$
• D. $\frac{5}{8}\text{m}$

Answer 1

The correct option is C $\frac{1}{8}\text{m}$

Displacement of particles of the medium near the wall will be zero. So, the minimum distance $d$ between the wall and the particles of the medium having maximum displacement during their vibrations will be $\frac{\lambda }{4}$ as we can see in the image below.

So, $d=\frac{\lambda }{4}$


We know that velocity of sound wave is given by,

$v=\lambda f$

where $\lambda$ is wavelength and $f$ is frequency.

$\Rightarrow \lambda =\frac{v}{f}$

$\Rightarrow \lambda =\frac{300}{600}=\frac{1}{2}\text{m}$

Now,

$d=\frac{\lambda }{4}=\frac{1}{2\times 4}=\frac{1}{8}\text{m}$