Question

Discuss the following case-

Observer in motion and Source at rest.

1. Observer moves towards Source
2. Observer resides away from the Source

Answer 1

(a) Observer moves towards Source:

Observer moves towards Source

We can assume that the observer O moves towards the source S with velocity v_o. 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 v_o and v are in opposite direction. Then, their relative velocity is v_r = v + v_o. 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 v_r = 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)