Question

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

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

Answer 1

Answer: (B)

No. of beats per second $=\frac{9}{3}=3\, s^{-1}$
No. of beats per second $=\upsilon_{1}-\upsilon_{2}$
$3=\frac{v}{\lambda_{1}}-\frac{v}{\lambda_{2}}=v \left[\frac{1}{\lambda_{1}}-\frac{1}{\lambda_{2}}\right]
\frac{3}{300}=\frac{1}{2}-\frac{1}{\lambda_{2}}$
$\frac{1}{\lambda_{2}}=\frac{1}{2}-\frac{1}{100}=\frac{50-1}{100}=\frac{49}{100}$
$\lambda_{2}=\frac{100}{49}$
$=2.04\,m$