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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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