Question

Two sound waves of wavelength $1\text{m}$ and $1.01\text{m}$ in a gas produce $10$ beats in $3\text{s}$. The velocity of sound in the gas is

• A. $330\text{m/s}$
• B. $337\text{m/s}$
• C. $360\text{m/s}$
• D. $300\text{m/s}$

Answer 1

The correct option is B $337\text{m/s}$

Given that $10$ beats in $3\text{s}$

So, $f_B=\frac{10}{3}\text{beats}$

We know that,
$f_B=|f_1-f_2|\dots \dots \left(1\right)$

Also,
$v=\lambda f\Rightarrow f=\frac{v}{\lambda }\dots \dots \left(2\right)$

From Eqs. (1) and (2)

$f_B=\frac{v}{{\lambda }_1}-\frac{v}{{\lambda }_2}$

[Speed $\left(v\right)$ of sound will be same as medium is same]

$\Rightarrow \frac{10}{3}=v[\frac{1}{1}-\frac{1}{1.01}]$

$\Rightarrow \frac{10}{3}=\frac{v}{101}$

$\Rightarrow v=336.67\text{m/s}\approx 337\text{m/s}$

Hence, option $\left(b\right)$ is the correct answer.