Question

A sound wave of frequency $500\text{Hz}$ covers the distance of $1000\text{m}$ in $5\text{s}$ between points $x$ and $y$. The number of wavelengths between $x$ and $y$ are

• A. $1500$
• B. $1000$
• C. $2500$
• D. $5000$

Answer 1

The correct option is C $2500$


Time taken by wave to cover distance $xy$ is $\Delta t=5\text{s}$
So, velocity of wave,
$v=\frac{\Delta x}{\Delta t}=\frac{1000}{5}=200\text{m/s}$
Now, wavelength of wave,
$\lambda =\frac{v}{f}=\frac{200}{500}=0.4\text{m}$
Let the number of wavelengths between $x$ and $y$ is $n$.
So, $n\lambda =\Delta x$
$\Rightarrow n=\frac{\Delta x}{\lambda }=\frac{1000}{0.4}$
$\therefore n=2500$