A rockel is receding away from earth with velocity =0.2 c . The rocket emits signal or frequency 4 × 107 Hz. The apparent frequency of the signal produced by the rocket observed by the observer on earth will be

Question

A rockel is receding away from earth with velocity =0.2 c . The rocket emits signal or frequency 4 × 107 Hz. The apparent frequency of the signal produced by the rocket observed by the observer on earth will be (A) 3 × 106 Hz (B) 4 × 106 Hz (C) 2.4 × 107 Hz (D) 5 × 107 Hz

Tardigrade Admin · Accepted Answer

As v=(1/2) (Δ v/v) c ∴ 0.2 c =(1/2) (Δ v /(4 × 107)) c Δ v =1.6 × 107 Hz As the rocket is receding away ∴ v'=v-Δ v=4 × 107-1.6 × 107 =2.4 × 107 Hz

Q. A rockel is receding away from earth with velocity $= 0.2 c .$ The rocket emits signal or frequency $4 \times 1 0^{7} Hz$ . The apparent frequency of the signal produced by the rocket observed by the observer on earth will be

$3 \times 1 0^{6} Hz$

$4 \times 1 0^{6} Hz$

$2.4 \times 1 0^{7} Hz$

$5 \times 1 0^{7} Hz$

As $v = \frac{1}{2} \frac{Δ v}{v} c$
$∴ 0.2 c = \frac{1}{2} \frac{Δ v}{( 4 \times 1 0 ^{7} )} c$
$Δ v = 1.6 \times 1 0^{7} Hz$
As the rocket is receding away
$∴ v^{'} = v - Δ v = 4 \times 1 0^{7} - 1.6 \times 1 0^{7}$
$= 2.4 \times 1 0^{7} Hz$

Q. A rockel is receding away from earth with velocity =0.2c. The rocket emits signal or frequency 4×107Hz. The apparent frequency of the signal produced by the rocket observed by the observer on earth will be

3×106Hz

4×106Hz

2.4×107Hz

5×107Hz