Calculating Relativistic Doppler Shift for Moving Radar

AI Thread Summary
The discussion focuses on calculating the relativistic Doppler shift for a radar detecting a car approaching at 135 km/h. The user converted the speed to meters per second and applied the Doppler shift formula, resulting in an unexpectedly large frequency difference of 1.024 x 10^13 Hz. Other participants noted that the formula used is correct, but the resulting value seems unrealistic due to the small ratio of v/c, which may not yield a significant frequency shift. They suggested using a Taylor expansion for small values of v/c to obtain a more accurate result. The conversation emphasizes the importance of proper calculations in relativistic contexts.
fluidistic
Gold Member
Messages
3,928
Reaction score
272

Homework Statement


A car is getting closer to a radar as a speed of 135 km/h. If the radar works at a 2 \times 10 ^{9} Hz, what difference of frequency is observed for the radar?

Homework Equations


\mu=\frac{\mu _0 \sqrt {1- \frac{v^2}{c^2}}}{1-\frac{v}{c}}

The Attempt at a Solution


I converted 135 km/h into m/s, which gave me \frac { 1350 m }{36 s}.
Then I applied the formula and \mu - \mu _0 gave me 1.024 \times 10^{13} Hz which seems WAY too big to be realistic. Am I missing something? Is it a wrong formula?!
 
Physics news on Phys.org
The formula is correct and I agree the number is way too large. Can you show how you got it? A word of caution: v/c is too small to plug in a calculator and expect something other than μ0, i.e. no frequency shift. I suggest that you try a Taylor expansion for small values of v/c.
 
Thread 'Collision of a bullet on a rod-string system: query'

Thread 'Collision of a bullet on a rod-string system: query'

In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
View full post »
Thread 'A cylinder connected to a hanged mass'

Thread 'A cylinder connected to a hanged mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

How do you calculate wind speed using the Doppler effect?
Replies
4
Views
3K
Doppler effect and acceleration of source
Replies
5
Views
2K
Doppler effect and beat frequency
Replies
3
Views
2K
Doppler Shift/ Doppler effect HELP
Replies
5
Views
3K
Calculating Doppler Shift for Radar Gun and Moving Ambulance
Replies
1
Views
3K
Doppler effect train frequency question
Replies
4
Views
2K
Blood flow velocity via Doppler effect
Replies
1
Views
2K
Doppler Effect: Velocity of a train
Replies
4
Views
2K
Moving vehicles and Doppler Effect
Replies
9
Views
7K
Difference between a clock and a series of radar pulses
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top