Hydr0matic said:What is the difference in magnitude between the effects of normal doppler effect and doppler effect in accelerated frames, e.g. when the (light)source is accelerating wrt the observer? What is the formula for doppler effect in accelerating frames?
Surely, doppler shift from a lightsource with relativistic and extremely accelerating speed isn't governed by the classical doppler formula?Relativity must be taken into account for the optical Doppler effect, since light, with its velocity of c, is an essentially relativistic object.
Hydr0matic said:By normal I mean with constant relative speed.
Surely, doppler shift from a lightsource with relativistic and extremely accelerating speed isn't governed by the classical doppler formula?
The Doppler Effect in accelerating frames refers to the change in frequency and wavelength of a wave when the source or observer is accelerating. This is different from the normal Doppler Effect, which only takes into account the relative motion between the source and observer.
The Doppler Effect in accelerating frames is calculated using the general formula for the Doppler Effect, which takes into account the acceleration of the source or observer. This formula is:
Δf/f = [(v/c) + (a/c)t]-1
Where Δf is the change in frequency, f is the original frequency, v is the relative velocity between the source and observer, c is the speed of the wave, a is the acceleration of the source or observer, and t is the time interval.
One example is the change in frequency of a siren on an accelerating ambulance. As the ambulance moves towards or away from an observer, the frequency of the siren will change due to the acceleration of the ambulance. Another example is the redshift and blueshift observed in the light from distant galaxies, which can be explained by the Doppler Effect in accelerating frames caused by the expansion of the universe.
The Doppler Effect in accelerating frames affects sound and light waves differently because they have different speeds. Sound waves travel at a much slower speed than light waves, so the acceleration of the source or observer has a greater impact on the frequency and wavelength of sound waves compared to light waves. Additionally, the Doppler Effect for light waves is also affected by the relative motion of the source and observer due to the constant speed of light.
Yes, the Doppler Effect in accelerating frames can be observed in everyday life. As mentioned before, the change in frequency of a siren on an accelerating ambulance is one example. Other examples include the change in frequency of a car horn as it accelerates towards or away from an observer, or the change in frequency of a train whistle as it rounds a corner. Additionally, the Doppler Effect in accelerating frames is also used in various technologies, such as radar and sonar systems.