Question

Two wave of wavelength 1.00 m and 1.01 m produce 10 beats in 3 s in a gas. The speed of sound in the gas will be

• A. $316.6m{s}^{-1}$
• B. $336.6m{s}^{-1}$
• C. $356.6m{s}^{-1}$
• D. $396.6m{s}^{-1}$

Answer 1

The correct option is B $336.6m{s}^{-1}$

Let,

The wavelengths of two waves are ${\lambda }_1$ and ${\lambda }_2$,

The frequencies of two waves are ${\nu }_1$ and ${\nu }_2$,

${\nu }_1=\frac{v}{{\lambda }_1}$

and

${\nu }_2=\frac{v}{{\lambda }_2}$

where, v is the speed of sound in the gas.

The frequency of beats is

${\nu }_1-{\nu }_2=\frac{v}{{\lambda }_1}-\frac{v}{{\lambda }_2}=\frac{10}{3}$

$\frac{v}{1}-\frac{v}{1.01}=\frac{10}{3}$ ...................(given)

$\frac{0.01v}{1.01}=\frac{10}{3}$

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

$v=\frac{1010}{3}=336.6Hz$