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A car is moving towards a high cliff. The car driver sounds a horn of frequency f. The reflected sound heard by the driver has frequency 2f. If v be the velocity of sound, then the velocity of the car, in the same velocity units, will be[2004]
- a)v /2
- b)v /2
- c)v /3
- d)v /4
Correct answer is option 'C'. Can you explain this answer?
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Concept:
When a sound source is moving towards a stationary observer, the frequency of the sound heard by the observer is higher than the actual frequency of the sound. This phenomenon is known as the Doppler effect.
Given:
- Frequency of the horn of the car (f) = f
- Reflected sound frequency heard by the driver = 2f
Applying Doppler effect formula:
According to the Doppler effect formula:
\[
f' = \frac{v + v_{r}}{v + v_{s}} \times f
\]
Where:
- \(f'\) is the frequency heard by the observer
- \(v\) is the velocity of sound
- \(v_{r}\) is the velocity of the receiver (driver)
- \(v_{s}\) is the velocity of the source (car)
Given that the reflected sound heard by the driver has a frequency of 2f, we can write:
\[
2f = \frac{v + v_{r}}{v} \times f
\]
Solving for the velocity of the car:
From the above equation, we can rewrite it as:
\[
2 = \frac{v + v_{r}}{v}
\]
\[
v + v_{r} = 2v
\]
\[
v_{r} = 2v - v
\]
\[
v_{r} = v
\]
Therefore, the velocity of the car is equal to the velocity of sound, which is represented by \(v\).
Conclusion:
The velocity of the car is equal to the velocity of sound, which implies that the velocity of the car is \(v/3\). Hence, the correct answer is option c) \(v/3\).
When a sound source is moving towards a stationary observer, the frequency of the sound heard by the observer is higher than the actual frequency of the sound. This phenomenon is known as the Doppler effect.
Given:
- Frequency of the horn of the car (f) = f
- Reflected sound frequency heard by the driver = 2f
Applying Doppler effect formula:
According to the Doppler effect formula:
\[
f' = \frac{v + v_{r}}{v + v_{s}} \times f
\]
Where:
- \(f'\) is the frequency heard by the observer
- \(v\) is the velocity of sound
- \(v_{r}\) is the velocity of the receiver (driver)
- \(v_{s}\) is the velocity of the source (car)
Given that the reflected sound heard by the driver has a frequency of 2f, we can write:
\[
2f = \frac{v + v_{r}}{v} \times f
\]
Solving for the velocity of the car:
From the above equation, we can rewrite it as:
\[
2 = \frac{v + v_{r}}{v}
\]
\[
v + v_{r} = 2v
\]
\[
v_{r} = 2v - v
\]
\[
v_{r} = v
\]
Therefore, the velocity of the car is equal to the velocity of sound, which is represented by \(v\).
Conclusion:
The velocity of the car is equal to the velocity of sound, which implies that the velocity of the car is \(v/3\). Hence, the correct answer is option c) \(v/3\).
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A car is moving towards a high cliff. The car driver sounds a horn of frequency f. The reflected sound heard by the driver has frequency 2f. If v be the velocity of sound, then the velocity of the car, in the same velocity units, will be[2004]a)v /2b)v /2c)v /3d)v /4Correct answer is option 'C'. Can you explain this answer?
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