Question

The wavelengths of $60cm$ and $61cm$, produce $9beats/sec$. The velocity of sound is (approximately)

• A. $330m/s$
• B. $335m/s$
• C. $340m/s$
• D. $325m/s$

Answer 1

The correct option is A

$330m/s$

Step 1: Given data

$$\begin{gathered} {\lambda }_1=60cm=0.6m \\ {\lambda }_2=61cm=0.61m \\ Beats=9beats/second \end{gathered}$$

Here,

${\lambda }_1,{\lambda }_2$denote the wavelength of waves.

Step 2: Formula used

Beats are calculated using the difference in frequency,

$$\begin{gathered} Beats=f_1-f_2 \\ f=\frac{v}{\lambda } \end{gathered}$$

Here,

$v=speedofsound$ , $f=frequency$

Step 3: Calculating the speed of sound

$$\begin{gathered} f_1=\frac{v}{{\lambda }_1} \\ {f}_2=\frac{v}{{\lambda }_2} \\ Beats=f_1-f_2 \\ Beats=\frac{v}{{\lambda }_1}-\frac{v}{{\lambda }_2} \\ Beats=v(\frac{1}{{\lambda }_1}-\frac{1}{{\lambda }_2}) \\ 9=v(\frac{1}{0.6}-\frac{1}{0.61}) \\ v=329.4m/s \end{gathered}$$

Hence, option A is correct, the speed of sound is approximately equal to $330m/s$.