The Doppler Effect in Sound Waves
, your friend Ken has come up with another article ..but this time its even more interesting .
The Doppler effect is a phenomenon observed whenever the source of waves is moving with respect to an observer. The Doppler effect can be described as the effect produced by a moving source of waves in which there is an apparent upward shift in frequency for the observer and the source are approaching and an apparent downward shift in frequency when the observer and the source is receding. The Doppler effect can be observed to occur with all types of waves - most notably water waves, sound waves, and light waves.Well guys , here I am keeping the topic to be for sound waves .
The Doppler effect is observed because the distance between the source of sound and the observer is changing. If the source and the observer are approaching, then the distance is decreasing and if the source and the observer are receding, then the distance is increasing. The source of sound always emits the same frequency. Therefore, for the same period of time, the same number of waves must fit between the source and the observer. if the distance is large, then the waves can be spread apart; but if the distance is small, the waves must be compressed into the smaller distance. For these reasons, if the source is moving towards the observer, the observer perceives sound waves reaching him or her at a more frequent rate (high pitch). And if the source is moving away from the observer, the observer perceives sound waves reaching him or her at a less frequent rate (low pitch). It is important to note that the effect does not result because of an actual change in the frequency of the source. The source puts out the same frequency; the observer only perceives a different frequency because of the relative motion between them. The Doppler effect is a shift in the apparent or observed frequency and not a shift in the actual frequency at which the source vibrates.
Consider a frame of reference in which the medium of signal propagation is assumed to be at rest, and suppose an emitter and absorber are located on the x axis, with the emitter moving to the left at a speed of ve and the absorber moving to the right, directly away from the emitter, at a speed of va. Let cs denote the speed at which the signal propagates with respect to the medium. Then, according to the classical (non-relativistic) treatment, the Doppler frequency shift is
( source -> www.grc.nasa.gov & hyperphysics.phy-astr.gsu.edu )
The Doppler shift of plane light waves in vacuum which arrive with an angle phi with respect to the direction of travel is:
The difference in the classical and relativistic Doppler effects can be seen in the following graph showing the wavelength shift of green light for velocities ranging from v/c=-1 (recession at the speed of light) to v/c=1 (approach at the speed of light). The Doppler shift predicted by classical physics is shown in red and the correct prediction of special relativity in green.
The overlapping of the two curves in the middle of the graph, where velocities are relatively small compared to the speed of light, demonstrates how relativistic effects have little impact at velocities below a substantial fraction of the speed of light. Note how the interaction of the classical Doppler shift and Lorentz contraction affects the two ends of the graph in different ways. For extreme approach velocities, relativity predicts a blue shift diverging toward infinity while the classical equation only halves the wavelength at rest. For large velocities of recession, both classical and relativistic equations show the wavelength approaching infinitely long values; here the Lorentz contraction reduces the amount of the Doppler shift while leaving intact the trend toward infinite wavelength.
I think its enough for u guys to perfectly have a pictorial idea of doppler effect .Anyways , enjoy the concept and closing....... with fond affection , your lovely friend Ken ..will be back with another one soon .