Question

Calculate the speed of sound in a gas in which two waves of wavelength 1.00m and 1.01m produce 30beats in 10seconds

• A. 300 m/s
• B. 303 m/s
• C. 310 m/s
• D. 313 m/s

Answer 1

The correct option is B 303 m/s

Number of beats per second $=\frac{30}{10}=3/s$
$v=f_1{\lambda }_1\Rightarrow f_1=\frac{v}{{\lambda }_1}$
$v=f_2{\lambda }_2\Rightarrow f_2=\frac{v}{{\lambda }_2}$
$f_1>f_2(\because {\lambda }_1<{\lambda }_2)$
$f_1-f_2=3;\frac{v}{{\lambda }_1}-\frac{v}{{\lambda }_2}=3$
$v=[\frac{1}{{\lambda }_1}-\frac{1}{{\lambda }_2}]=3;[\frac{1}{1}-\frac{1}{1.01}]=3;\left[\frac{0.01}{1.01}\right]=3$
$v=\frac{3.03}{0.01}=303m{s}^{-1}$