Question

a source of electromagnetic radiation is moving in a radial di- rection relative to you. the frequency you measure is 1.25 times the fre- quency measured in the rest frame of the source. what is the speed of the source relative to you? is the source moving toward you or away from you?

Answer 1

The speed of the source relative to you is approximately 0.111 times the speed of light. The source is moving away from you.

Step-by-step explanation:

The observed frequency of electromagnetic radiation undergoes a Doppler shift when the source is moving relative to the observer. If the frequency you measure is 1.25 times the frequency measured in the rest frame of the source, we can use the equation for the Doppler shift to find the speed of the source relative to you.

The equation is given by:

f' = (c+v)/(c-v) * f

where:

• f' is the observed frequency
• c is the speed of light
• v is the speed of the source relative to you
• f is the frequency measured in the rest frame of the source

Let's substitute the given values into the equation:

1.25f = (c+v)/(c-v) * f

Now we can solve for v:

1.25 = (c+v)/(c-v)

1.25(c-v) = c+v

1.25c - 1.25v = c+v

0.25c = 2.25v

v = 0.25c / 2.25

v ≈ 0.111c

Since the value for v is positive, it means the source is moving away from you.

Answer 2

The observed frequency is 1.25 times the rest frequency due to the relativistic Doppler effect, indicating a blue shift and that the source is moving towards the observer. The speed of the source can be determined by the frequency ratio.

Step-by-step explanation:

When a source of electromagnetic radiation is moving in a radial direction relative to an observer, the observed frequency of the radiation can change due to the relativistic Doppler effect. If the observer measures a frequency that is 1.25 times the frequency measured in the rest frame of the source, we refer to this as a blue shift, indicating that the source is moving towards the observer.

To calculate the speed of the source relative to the observer, we can use the relativistic Doppler shift formula, which relates the observed frequency to the emitted frequency and the velocity of the source. Since the frequency observed is higher, the source must be moving toward the observer, and we can derive the velocity using the given frequency ratio.