Question:
A person at rest hears an electric siren which is stationary. Now the person accelerates at \(2\,\text{m s}^{-2}\) along a straight line path. The distance travelled by him when he hears the frequency of the siren as \(94\%\) of its original value is \((\text{speed of sound} = 330\,\text{m s}^{-1})\):
A person at rest hears an electric siren which is stationary. Now the person accelerates at \(2\,\text{m s}^{-2}\) along a straight line path. The distance travelled by him when he hears the frequency of the siren as \(94\%\) of its original value is \((\text{speed of sound} = 330\,\text{m s}^{-1})\):
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For Doppler effect involving moving observer:
\[
f'=f\left(\frac{v\pm v_o}{v}\right)
\]
Use minus sign when observer moves away from source.
Updated On: Jun 17, 2026
- \(49\,\text{m}\)
- \(98\,\text{m}\)
- \(147\,\text{m}\)
- \(196\,\text{m}\)
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The Correct Option is B
Solution and Explanation
Concept:
For a moving observer and stationary source, the apparent frequency is:
\[
f' = f\left(\frac{v-v_o}{v}\right)
\]
where:
• \(v\) = speed of sound,
• \(v_o\) = speed of observer,
• \(f\) = original frequency,
• \(f'\) = observed frequency.
Step 1: Use the given frequency condition. Given: \[ f' = 0.94f \] Thus, \[ 0.94f = f\left(\frac{330-v_o}{330}\right) \] Cancelling \(f\): \[ 0.94 = \frac{330-v_o}{330} \] \[ 310.2 = 330-v_o \] \[ v_o = 19.8 \approx 20\,\text{m s}^{-1} \]
Step 2: Use equation of motion. Initial velocity: \[ u=0 \] Acceleration: \[ a=2\,\text{m s}^{-2} \] Using: \[ v^2=u^2+2as \] \[ 20^2=0+2(2)s \] \[ 400=4s \] \[ s=100\,\text{m} \] Closest option: \[ \boxed{98\,\text{m}} \]
• \(v\) = speed of sound,
• \(v_o\) = speed of observer,
• \(f\) = original frequency,
• \(f'\) = observed frequency.
Step 1: Use the given frequency condition. Given: \[ f' = 0.94f \] Thus, \[ 0.94f = f\left(\frac{330-v_o}{330}\right) \] Cancelling \(f\): \[ 0.94 = \frac{330-v_o}{330} \] \[ 310.2 = 330-v_o \] \[ v_o = 19.8 \approx 20\,\text{m s}^{-1} \]
Step 2: Use equation of motion. Initial velocity: \[ u=0 \] Acceleration: \[ a=2\,\text{m s}^{-2} \] Using: \[ v^2=u^2+2as \] \[ 20^2=0+2(2)s \] \[ 400=4s \] \[ s=100\,\text{m} \] Closest option: \[ \boxed{98\,\text{m}} \]
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