Two sound waves having wavelengths $5.0 \mathrm{~m}$ and $5.5 \mathrm{~m}$ propagates in a gas with velocity…

Two sound waves having wavelengths $5.0 \mathrm{~m}$ and $5.5 \mathrm{~m}$ propagates in a gas with velocity $300 \mathrm{~m} / \mathrm{s}$. The number of beats produced per second is
  1. six
  2. two
  3. three
  4. one

Solution

$\begin{aligned} & \lambda_1=5.0 \mathrm{~m} \text { and } \lambda_2=5.5 \mathrm{~m}, \mathrm{v}=300 \mathrm{~m} / \mathrm{s} \\ & \mathrm{n}_1=\frac{\mathrm{V}}{\lambda_1}=\frac{300}{5}=60 \mathrm{~Hz} \\ & \mathrm{n}_2=\frac{\mathrm{V}}{\lambda_2}=\frac{300}{5.5}=54.5 \mathrm{~Hz} \simeq 54 \mathrm{~Hz} \end{aligned}$ Number of beats $=\mathrm{n}_1-\mathrm{n}_2=60-54=6 \mathrm{~Hz}$

Asked in: MHT CET 2021 (24 Sep Shift 1)

Practice more Waves and Sound questions on Aicharya