Question

Sound wave of frequency $600\text{Hz}$ fall normally on a perfect reflecting wall. The minimum distance from the wall at which particles of the medium will have maximum displacement during its 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 wall will be zero, hence minimum distance $d$ from wall of particles of the medium having maximum displacement during its vibrations will be $\frac{\lambda }{4}$.
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,
$d=\frac{\lambda }{4}=\frac{1}{2\times 4}=\frac{1}{8}\text{m}$