Question

The wavelengths of two notes in the air are $\frac{36}{195} \, m$ and $\frac{36}{193} \, m$ . Each note produces $10$ beats per second separately with a third note of fixed frequency. The velocity of sound in air in $m \, s^{- 1}$ is

• A. $330$
• B. $340$
• C. $350$
• D. $360$

Answer 1

Answer: (D)

Beat frequency= $v_{1}\sim v_{2}$
Let the frequency of third note be $n$ .
Then,
$\frac{195 v}{36}-n=10 \, \, \ldots \left(i\right)$
And
$n-\frac{193 v}{36}=10 \, \ldots \left(i i\right)$
Adding Eqs. (i) and (ii)
$\frac{v}{18}=20$
$\Longrightarrow \, \, v=360 \, ms^{- 1}$