Energy loss in the doppler effect?

[p.tryon]

If the energy of an EM wave = h x f
and when a light emitting body (of a particular power) is moving toward or away from the observer the observed frequency changes, does the energy change?
If so where does the gained or lost energy come from?

 

[Hootenanny]

Energy, is of course, reference frame dependent. Consider the classical scenario of two cars traveling towards each other along a road, you are sat in one car. Each car is traveling at 30mph relative to an observer who is stood stationary on the road.

Now, if you (sat in your car) 'measure' the kinetic energy of the other car is it going to be the same as if the stationary observer 'measures' the kinetic energy of the other car?

 

[sir-pinski]

The energy of an electromagnetic (EM) wave is directly proportional to its frequency, as given by the equation E = hf, where h is Planck's constant and f is the frequency. In the case of the Doppler effect, the frequency of the EM wave changes when the source of the wave is moving towards or away from the observer. However, this change in frequency does not necessarily mean a change in energy.

The energy of an EM wave is determined by the source of the wave and remains constant regardless of the observer's position. Therefore, the energy of the wave does not change due to the Doppler effect. The change in frequency is simply a result of the relative motion between the source and the observer.

It is important to note that the power of the light emitting body also does not change due to the Doppler effect. The power is a measure of the rate at which energy is transferred, and since the energy of the EM wave remains constant, the power also remains constant.

In conclusion, the energy loss in the Doppler effect does not occur as the energy of the EM wave remains constant. The change in frequency is a result of relative motion and does not affect the energy or power of the wave. Therefore, no energy is gained or lost in the Doppler effect.