Question

Two sound waves of wavelengths $1m$ and $1.01m$ produce $10$ beats in $3$ seconds. Then, the velocity of the sound is

• A. $330m{s}^{-1}$
• B. $333.3m{s}^{-1}$
• C. $336.7m{s}^{-1}$
• D. none of the above

Answer 1

The correct option is C $336.7m{s}^{-1}$

From the formula, $v=f\lambda$

and the velocity of the sound in air is frequency independent.

for two frequencies $f_1$ and $f_2$, wavelengths are ${\lambda }_1$

and ${\lambda }_2$ , then the beats will be

$f_1-f_2=v(\frac{1}{{\lambda }_1}-\frac{1}{{\lambda }_2})=v\left(\frac{{\lambda }_2-{\lambda }_1}{{\lambda }_2{\lambda }_1}\right)$
$\frac{10}{3}=v\left(\frac{0.01}{1.0\times 1.01}\right)$
$v=\frac{10\times 1.0\times 1.01}{3.0\times 0.01}=336.66{\text{ms}}^{-1}$

Option "C" is correct.