How do you find speed given the beat frequency?

[Ekullabran]

Homework Statement

Using a radar gun, you emit radar waves at a frequency of 2.6 GHz that bounce off of a moving tennis ball and recombine with the original waves. This produces a beat frequency of 730 Hz. How fast was the tennis ball moving?

Homework Equations

fbeat = fa - fb
v=λf
f=1/T

The Attempt at a Solution

I found the frequency that bounces back from the moving tennis ball using fbeat=fa-fb, however, I don't know how to find that speed of the tennis ball given that I don't know its wavelength.

 

[TSny]

Hello.

Homework Statement

... I don't know how to find that speed of the tennis ball given that I don't know its wavelength.

What wavelength are you referring to here?

Start with the concept of why there is a change in wavelength when the radar waves bounce off the tennis ball. There is a name for the phenomenon of this type of frequency shift. (The name starts with "D"). Your list of relevant equations should include an equation or two related to this phenomenon.

I guess you are to assume that the ball is traveling directly toward or away from the radar gun rather than traveling at some oblique angle to the direction of propagation of the radar waves. Otherwise, there would not be enough information given in the problem.

 

[Ekullabran]

Hi!

Hello.
What wavelength are you referring to here?

Start with the concept of why there is a change in wavelength when the radar waves bounce off the tennis ball. There is a name for the phenomenon of this type of frequency shift. (The name starts with "D"). Your list of relevant equations should include an equation or two related to this phenomenon.

I guess you are to assume that the ball is traveling directly toward or away from the radar gun rather than traveling at some oblique angle to the direction of propagation of the radar waves. Otherwise, there would not be enough information given in the problem.

I am assuming you are referring to the doppler effect if so I would assume you would use fapparent = (v/(vs+v))f. Would this be sufficient enough to solve this question?

 

[TSny]

Hi!
I am assuming you are referring to the doppler effect..

Yes

...if so I would assume you would use fapparent = (v/(vs+v))f. Would this be sufficient enough to solve this question?

It's a little more complicated. The source of the waves is the radar gun, and it is at rest. The frequency shift occurs when the waves bounce off the moving ball. The ball first "receives" the waves and then acts as a "source" in sending the waves back to the gun. The ball acts both as a receiver (or "observer") and as a source. So, you need to combine the doppler formula for a moving observer with the doppler formula for a moving source. Or, hopefully, you've already covered the doppler shift formula for waves reflecting off a moving object.

For derivation see https://www.khanacademy.org/science...doppler-effect-reflection-off-a-moving-object

If you just want the formula without the derivation see https://en.wikipedia.org/wiki/Doppler_radar