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Question
Discuss the following case-
Observer in motion and Source at rest.
- Observer moves towards Source
- Observer resides away from the Source
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Solution
(a) Observer moves towards Source:
Observer moves towards Source
We can assume that the observer O moves towards the source S with velocity vo. The source S is at rest and the velocity of sound waves (with respect to the medium) produced by the source is v.
From the Figure, It is observed that both vo and v are in opposite direction. Then, their relative velocity is vr = v + vo. The wavelength of the sound wave is λ = `"v"/"f"`, which means the frequency observed by the observer O is f ‘ = `"v"_"r"/lambda`. Then
`"f"' = "v"_"r"/lambda = (("v" + "v"_0)/"v")"f"`
`= "f"(1 + "v"_0/"v")` ...(7)
(b) Observer recedes away from the Source:
If the observer O is moving away (receding away) from the source S, then velocity v0 and v move in the same direction. Hence, their relative velocity is vr = v – v0. Hence, the frequency observed by the observer O is
`"f"' = "v"_"r"/lambda = (("v" + "v"_0)/"v")"f"`
`= "f"(1 - "v"_0/"v")` ...(8)
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RELATED QUESTIONS
In discussing Doppler effect, we use the word "apparent frequency". Does it mean that the frequency of the sound is still that of the source and it is some physiological phenomenon in the listener's ear that gives rise to Doppler effect? Think for the observer approaching the source and for the source approaching the observer.
Answer briefly.
State the expression for apparent frequency when source of sound and listener are
- moving towards each other
- moving away from each other
What is meant by the Doppler effect?
Discuss the following case-
Both are in motion
- Source and Observer approach each other
- Source and Observer resides from each other
- Source chases Observer
- Observer chases Source
Two cars moving in opposite directions approach each other with speed of 22 m/s and 16.5 m/s respectively. The driver of the first car blows a horn having a frequency 400 Hz. The frequency heard by the driver of the second car is [velocity of sound 340 m/s]: ____________.
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