Question:
An observer moves towards a stationary source of sound with a velocity equal to one-fourth of the velocity of sound. Then the percentage increase in the apparent frequency observed by the observer is
An observer moves towards a stationary source of sound with a velocity equal to one-fourth of the velocity of sound. Then the percentage increase in the apparent frequency observed by the observer is
Show Hint
For a stationary source and moving observer,
\[
f'=f\left(1+\frac{v_o}{v}\right).
\]
Hence the percentage increase in frequency is simply
\[
\frac{v_o}{v}\times100.
\]
If \(v_o=\frac{v}{4}\), the increase is \(25\%\).
Updated On: Jul 29, 2026
- \(25\%\)
- \(20\%\)
- \(30\%\)
- \(50\%\)
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The Correct Option is A
Solution and Explanation
Concept:
For a stationary source and an observer moving towards the source, the apparent frequency is given by
\[
f' = f\left(\frac{v+v_o}{v}\right),
\]
where
\[
v=\text{velocity of sound},
\qquad
v_o=\text{velocity of observer}.
\]
Step 1: Write the given information. The observer moves with speed \[ v_o=\frac{v}{4}. \]
Step 2: Calculate the apparent frequency. Using Doppler's formula, \[ f' = f\left(\frac{v+\frac{v}{4}}{v}\right). \] \[ = f\left(\frac{5v}{4v}\right). \] \[ = \frac54 f. \]
Step 3: Find the percentage increase in frequency. Increase in frequency: \[ \Delta f = f'-f = \frac54f-f. \] \[ = \frac14f. \] Therefore, \[ \text{Percentage Increase} = \frac{\Delta f}{f}\times100. \] \[ = \frac14\times100. \] \[ = 25\%. \] Therefore, \[ \boxed{\text{Percentage increase}=25\%} \] \[ \boxed{\text{Answer = (A)}} \]
Step 1: Write the given information. The observer moves with speed \[ v_o=\frac{v}{4}. \]
Step 2: Calculate the apparent frequency. Using Doppler's formula, \[ f' = f\left(\frac{v+\frac{v}{4}}{v}\right). \] \[ = f\left(\frac{5v}{4v}\right). \] \[ = \frac54 f. \]
Step 3: Find the percentage increase in frequency. Increase in frequency: \[ \Delta f = f'-f = \frac54f-f. \] \[ = \frac14f. \] Therefore, \[ \text{Percentage Increase} = \frac{\Delta f}{f}\times100. \] \[ = \frac14\times100. \] \[ = 25\%. \] Therefore, \[ \boxed{\text{Percentage increase}=25\%} \] \[ \boxed{\text{Answer = (A)}} \]
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