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

Question

An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency 10 GHz. What is the frequency of the microwave measured by the observer ? (speed of light = 3 × 108 ms-1) (A) 10.1 GHz (B) 12.1 GHz (C) 17.3 GHz (D) 15.3 GHz

Tardigrade Admin · Accepted Answer

For relativistic motion f = f0 √(c+v/c-v) ; v = relative speed of approach f = 10√(c+(c/2)/c-(c)2) = 10√3 = 17.3 GHz

Q. An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency $10 G Hz$ . What is the frequency of the microwave measured by the observer ?
(speed of light $= 3 \times 1 0^{8} m s^{- 1}$ )

10.1 GHz

12.1 GHz

17.3 GHz

15.3 GHz

For relativistic motion
$f = f_{0} \frac{c + v}{c - v}$ ; v = relative speed of approach
$f = 10 \frac{c + \frac{c}{2}}{c - \frac{c}{2}} = 103 = 17.3 G Hz$

Q. 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)