Question

A highway patrol officer uses a device that measures the speed of vehicles by bouncing radar off them and measuring the Doppler shift. The outgoing radar has a frequency of 100 GHz and the returning echo has a frequency 15.0 kHz higher. What is the velocity of the vehicle? Note that there are two Doppler shifts in echoes. Be certain not to round off until the end of the problem, because the effect is small.

Answer 1

Answer:

$V = 2.5725*10^{-5}m/s$

Explanation:

The data we are given is:

V = ?     fo = 100GHz        fs = 100000015KHz    C = 343m/s

With the doppler effect formula we can calculate the frequency perceived by the vehicle as:

$fr = \frac{C+V}{C}*fo$     (1)

Then, we sound waves bounce back on the vehicle:

$fs = \frac{C}{C-V}*fr$      (2)   Replacing tha value obtained in (1)

$fs = \frac{C}{C-V}*\frac{C+V}{C}* fo$   Solving for V:

$V = C*\frac{fs-fo}{fs+fo}=2.5725*10^{-5}m/s$