MHT CET · Physics · Waves and Sound
An observer moves towards a stationary source of sound with a velocity of one-fifth of the velocity of sound. The percentage increase in the apparent frequency is
- A \(5 \%\)
- B \(10 \%\)
- C \(20 \%\)
- D \(25 \%\)
Answer & Solution
Correct Answer
(C) \(20 \%\)
Step-by-step Solution
Detailed explanation
When observer moves towards the stationary source then apparent frequency,
\(\mathrm{n}^{\prime}=\left(\frac{\mathrm{v}+\mathrm{v}_{\mathrm{o}}}{\mathrm{v}}\right) \mathrm{n}\)
Given, \(\mathrm{v}_{\mathrm{o}}=\mathrm{v} / 5\).
\(\therefore \quad \mathrm{n}^{\prime}=\left(\frac{\mathrm{v}+\frac{\mathrm{v}}{5}}{\mathrm{v}}\right) \mathrm{n}=\frac{6}{5} \mathrm{n}\)
Increase in apparent frequency \(=\mathrm{n}^{\prime}-\mathrm{n}=\frac{6}{5} \mathrm{n}-\mathrm{n}=\frac{1}{5} \mathrm{n} \Rightarrow 20 \%\) of n
\(\mathrm{n}^{\prime}=\left(\frac{\mathrm{v}+\mathrm{v}_{\mathrm{o}}}{\mathrm{v}}\right) \mathrm{n}\)
Given, \(\mathrm{v}_{\mathrm{o}}=\mathrm{v} / 5\).
\(\therefore \quad \mathrm{n}^{\prime}=\left(\frac{\mathrm{v}+\frac{\mathrm{v}}{5}}{\mathrm{v}}\right) \mathrm{n}=\frac{6}{5} \mathrm{n}\)
Increase in apparent frequency \(=\mathrm{n}^{\prime}-\mathrm{n}=\frac{6}{5} \mathrm{n}-\mathrm{n}=\frac{1}{5} \mathrm{n} \Rightarrow 20 \%\) of n
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