Question

A stationary receiver detects a change in frequency of the signal from a jet flying directly away from it at 300 m/s. Which of the following receivers will detect the same change in frequency from a jet moving away at 600 m/s?A) A receiver moving at 900 m/s in the opposite direction as the jetB) A receiver moving at 300 m/s in the opposite direction as the jetC) A stationary receiverD) A receiver moving at 300 m/s in the same direction as the jet

Answer 1

Answer:

d) the receiver should be moving at 300 m/s in the same direction as the jet.

Explanation:

The change in the frequency of a moving sound (or wave) source is called Doppler Effect. The change in frequency is:

$\Delta f=\frac{\Delta v}{v}f_{o}$ (1)

with $\Delta v=\mid v_{r}-v_{s}\mid$ the velocity of the receptor respect the source, $f_{o}$ the real frequency  and $v$ the velocity of the waves in the medium, we should be verty careful because the direction of the velocities are important so we have to select a reference frame and take on account the sign of the velocities. We're going to select positive direction as airplane direction. If we assume the frequency of the airplane sound and the velocity of waves on air remain constant, we should find the option that give us $\Delta v=\mid v_{r}-v_{s}\mid = 300$ as the stationary case; let's see for:

a) $\Delta v=\mid v_{r}-v_{s}\mid =\mid -900-600 \mid= 1500$

b) $\Delta v=\mid v_{r}-v_{s}\mid = \mid-300-600 \mid= 900$

c) $\Delta v=\mid v_{r}-v_{s}\mid = \mid0-600\mid = 600$

d) $\Delta v=\mid v_{r}-v_{s}\mid= \mid300-600\mid = 300$

So, the correct answer is d)