You are trying to communicate with a rocket ship that is traveling at 1.2 ×10^8 m / s away from

You are trying to communicate with a rocket ship that is...

Key Concepts

Relativistic Communication

In scenarios where objects such as rockets travel at significant fractions of the speed of light, standard communication theories are adapted to include relativistic effects. This involves calculating the correct received frequency by applying the relativistic Doppler formula, ensuring that the receiver can compensate for the effects of their high relative velocity.

Frequency Shift

Frequency is the number of cycles per unit time of a wave, and a frequency shift occurs when the source and observer are in relative motion. This shift must be taken into account in high-speed communications to ensure the receiver is tuned to the correct frequency, thereby correctly interpreting the transmitted signal.

Relativistic Doppler Effect

The relativistic Doppler effect describes how the observed frequency of a wave (such as an electromagnetic signal) shifts when there is a relative motion between the source and the observer at speeds comparable to the speed of light. Unlike the classical Doppler effect, this formulation accounts for time dilation, meaning that the moving clock ticks slower in the observer's frame, leading to a modification in the observed frequency.

Transcript

00:01 In this problem, we're going to be looking at the doppler shift of lights.

00:05 You've seen that in the past with sound, where because of the motion of a source, motion of an observer, that the frequency that the observer found was not the same as the source frequency, higher or lower depending on the motion.

00:23 And we'll talk about that more now for light in a second.

00:26 Now, first off, they give us the relative velocity between the source and the receiver is 1 .2 times 10 to 8 meters per second.

00:34 We divide that by c, 3 times 10 to 8.

00:38 We get the distance 0 .4c.

00:40 A minor point, but in the formulas, not having to punch in all the numbers, just cuts down a little bit on what you have to do there.

00:49 So now, for doppler shift of light, we have the following formula.

00:55 The frequency that is received is equal to frequency of the source, square root 1 minus v over c, 1 plus v over c.

01:05 As i said, v is the relative velocity between the source and the receiver, the observer.

01:18 And the v is greater than zero if they are receding, separating, and v is less than zero if they are approaching, getting closer together.

01:37 Now, let's talk about the connections and the differences with sound.

01:44 Sound there was a medium air so your velocities in those formulas were written relative to the air the medium where sound is needed to transmit sound there is no such medium for light that was the whole work at the beginning that led to special relativity michelson morley experiments you've talked about that certainly there's no ether there is no medium for the transmission of light so all you have is relative velocity that's it that's why it's all we have in here.

02:19 So that's the biggest change.

02:21 One other thing is not relevant to this problem, but just due to time dilation alone.

02:26 Remember, it would sound, it was motion either toward or away from the source.

02:35 You had motion along this line here.

02:39 Now, because of time dilation alone, if you have motion perpendicular, transverse, you also have a doppler shift.

02:50 So that's not something, that's solely due to relativity, special relativity, and time dilation.

02:59 Like i said, it's not part of this problem.

03:00 This problem is exactly the same as what you've done, longitudinal along this line here.

03:06 There's motion.

03:07 But i just wanted to make you aware of that.

03:11 So at this point, there's only putting in our values, 55 kilohertz, 10 to 3 hertz.

03:22 You don't have to convert that.

03:24 It'll come out in kilohertz, whatever answer you get...

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