Wave Motion 3 Question 3

3. An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency 10GHz. What is the frequency of the microwave measured by the observer? (speed of light =3×108ms−1 )

(2017 Main)

(a) 12.1GHz

(b) 17.3GHz

(c) 15.3GHz

(d) 10.1GHz

Show Answer

Answer:

Correct Answer: 3. (b)

Solution:

  1. As observer is moving with relativistic speed; formula Δff=vradial c, does not apply here.

Relativistic doppler’s formula is

fobserved =factual ⋅(1+v/c1−v/c)1/2

Here, vc=12

So, fobserved =factual (3/21/2)1/2

∴fobserved =10×3=17.3GHz

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