Question

Using a radar gun, you emit radar waves at a frequency of 6.2 GHz that bounce off of a moving tennis ball and recombine with the original waves. This produces a beat frequency of 969 Hz. How fast was the tennis ball moving?

Answer 1

Answer:

23.4 m/s

Explanation:

f = actual frequency of the wave = 6.2 x 10⁹ Hz

$f_{app}$ = frequency observed as the ball approach the radar

$f_{rec}$ = frequency observed as the ball recede away from the radar

V = speed of light

$v$ = speed of ball

B = beat frequency = 969 Hz

frequency observed as the ball approach the radar is given as

$f_{app}=\frac{f(V+v)}{V}$                                 eq-1

frequency observed as the ball recede the radar is given as

$f_{rec}=\frac{f(V-v)}{V}$                                  eq-2

Beat frequency is given as

$B = f_{app} - f_{rec}$

Using eq-2 and eq-1

$B = \frac{f(V+v)}{V}- \frac{f(V-v)}{V}$

inserting the values

$969 = \frac{(6.2\times 10^{9})((3\times 10^{8})+v)}{(3\times 10^{8})}- \frac{(6.2\times 10^{9})((3\times 10^{8})-v)}{(3\times 10^{8})}$

$v$ = 23.4 m/s