Question

The speed of sound in a gas, in which two waves of wavelength 1.0 m and 1.02 m produce 6 beats per second, is approximately:

• A. $350m/s$
• B. $300m/s$
• C. $380m/s$
• D. $410m/s$

Answer 1

Answer: (B)

$300m/s$

Let, $n_1$ and $n_2$ be the frequencies of two waves.

${\lambda }_1$ and ${\lambda }_2$ be the wavelengths of two waves.

$v$ be the speed of sound.

The number of beats per second are

$n_1-n_2=6$

$\frac{v}{{\lambda }_1}-\frac{v}{{\lambda }_2}=6$
$\frac{v}{1}-\frac{v}{1.02}=6$
$\frac{0.02v}{1.02}=6$

$0.02v=\left(6\right)\left(1.02\right)$
$v=\frac{6.12}{0.02}=306m{s}^{-1}\approx 300m/s$