MHT CET · Physics · Waves and Sound
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
- A six
- B two
- C three
- D one
Answer & Solution
Correct Answer
(A) six
Step-by-step Solution
Detailed explanation
\(
\begin{aligned}
& \lambda_1=5.0 \mathrm{~m} \text { and } \lambda_2=5.5 \mathrm{~m}, \mathrm{v}=300 \mathrm{~m} / \mathrm{s} \\
& \mathrm{n}_1=\frac{\mathrm{V}}{\lambda_1}=\frac{300}{5}=60 \mathrm{~Hz} \\
& \mathrm{n}_2=\frac{\mathrm{V}}{\lambda_2}=\frac{300}{5.5}=54.5 \mathrm{~Hz} \simeq 54 \mathrm{~Hz}
\end{aligned}
\)
Number of beats \(=\mathrm{n}_1-\mathrm{n}_2=60-54=6 \mathrm{~Hz}\)
\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 \(=\mathrm{n}_1-\mathrm{n}_2=60-54=6 \mathrm{~Hz}\)
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