Question

Two sound waves with wavelengths $5\text{m}$ and $5.5\text{m}$ respectively, propagates in a gas with velocity $330\text{m/s}$. The number of beats per second will be

• A. $6\text{Hz}$
• B. $15\text{Hz}$
• C. $17\text{Hz}$
• D. $19\text{Hz}$

Answer 1

The correct option is A $6\text{Hz}$

For first wave,
$f_1=\frac{v}{{\lambda }_1}$
$\Rightarrow f_1=\frac{330}{5}=66\text{Hz}$
For second wave,
$f_2=\frac{v}{{\lambda }_2}$
$\Rightarrow f_2=\frac{330}{5.5}=60\text{Hz}$
Now, beat frequency is
$f_b=f_1-f_2$
$\Rightarrow f_b=66-60$
$\Rightarrow f_b=6\text{Hz}$