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=3108 ms-1) a 10.1 ghz b 12.1 ghz c 17.3 ghz d 15.3 ghz

Answer 1

The frequency of the microwave measured by the observer will be option  c) 17.3 ghz

Explanation :

Given,

speed of light, C = 3 x 10⁸ m/s

frequency of microwave = 10 ghz

speed of observer = half the speed of light

=> V = C/2

=> V/C = 0.5

since the speed of observer is not negligible compared to speed of light, hence from doppler effect

frequency measured by the observer

= f₁ = f x $\sqrt{\frac{1 + V/C}{1 - V/C} }$

=> f₁ = 10 x √(1.5/0.5)

=> f₁ = 10 x √3 = 17.3 ghz

Hence the frequency of the microwave measured by the observer will be  c) 17.3 ghz