A source of sound S is moving with a velocity 50 m/s towards a station...
When the source is coming to stationary observer
When the source is moving away from stationary observer
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A source of sound S is moving with a velocity 50 m/s towards a station...
Given Information:
- Velocity of source (Vs) = 50 m/s (moving towards the observer)
- Frequency of source as measured by observer (f) = 1000 Hz
- Velocity of sound (V) = 350 m/s
To Find:
Apparent frequency of the source when it is moving away from the observer after crossing him.
Explanation:
When a source of sound is in motion relative to an observer, the frequency perceived by the observer is affected due to the Doppler effect. The Doppler effect states that the perceived frequency of a wave is different when the source and observer are moving relative to each other.
When the source is moving towards the observer, the frequency perceived by the observer is higher than the actual frequency of the source. This is known as the "Doppler shift towards higher frequency" or the "blueshift". The formula to calculate the apparent frequency (fa) in this case is given by:
fa = [(V + Vo)/(V - Vs)] * f
where,
fa = apparent frequency,
Vs = velocity of the source (moving towards the observer),
V = velocity of sound in the medium,
f = frequency of the source.
Calculation:
Given that Vs = 50 m/s, V = 350 m/s, and f = 1000 Hz.
Using the formula for apparent frequency, we can calculate the value of fa when the source is moving towards the observer:
fa = [(V + Vo)/(V - Vs)] * f
= [(350 + 0)/(350 - 50)] * 1000
= (350/300) * 1000
= 1.1667 * 1000
= 1166.7 Hz (approximately)
Therefore, when the source is moving towards the observer, the apparent frequency is approximately 1166.7 Hz.
When the source crosses the observer and starts moving away from them, the formula for apparent frequency changes:
fa = [(V - Vo)/(V + Vs)] * f
In this case, the velocity of the source (Vs) becomes negative (-50 m/s) as it is moving away from the observer.
Substituting the values into the formula:
fa = [(350 - 0)/(350 + 50)] * 1000
= (350/400) * 1000
= 0.875 * 1000
= 875 Hz
Therefore, when the source is moving away from the observer, the apparent frequency is 875 Hz.
Conclusion:
The apparent frequency of the source when it is moving away from the observer after crossing him is 875 Hz.