Question

A sound wave travels with a velocity of $300m{s}^{-1}$ through a gas. $9$ beats are produced in $3s$ when two waves pass through it simultaneously. If one of the wave has $2m$ wavelength, the wavelength of the other wave is :

• A. $1.98m$
• B. $2.04m$
• C. $2.06m$
• D. $1.99m$

Answer 1

The correct option is B $2.04m$

no. of beats per second $=\frac{9}{3}=3s^{-1}$
no. of betas per second $={\nu }_1-{\nu }_2$
$3=\frac{v}{{\lambda }_1}-\frac{v}{{\lambda }_2}=v[\frac{1}{{\lambda }_1}-\frac{1}{{\lambda }_2}]$
$\frac{3}{300}=\frac{1}{2}-\frac{1}{{\lambda }_2}$
$\frac{1}{{\lambda }_2}=\frac{1}{2}-\frac{1}{100}=\frac{50-1}{100}=\frac{49}{100}$
${\lambda }_2=\frac{100}{49}=2.04m$