I have a problem in regard to the doppler effect,which may be generalised to all waves--sound,water etc. Please explain why the observed frequency increases as the object approaches an observer and then decreases as the object passes the observer.Actually,I thought that since doppler effect depends only on the relative velocity between observer and source,the observed frequency should be constant throughout the process,as the relative velocity does not change as the distance between the source and observer changes. I also found on a website that it said that 'the observed frequency of an approaching object declines monotonically from a value above the emitted frequency, through a value equal to the emitted frequency when the object is closest to the observer, and to values increasingly below the emitted frequency as the object recedes from the observer'---Does this mean the same thing as what I asked at the begginning or is it different? Also,does the intensity of the sound increase as an object approaches an observer and decrease once it passes and recedes from the observer?
I think you're assuming that the object is heading straight for the observer. In practice, it usually misses the observer, and so the relative speed does change continuously. Yes.
Adding to tiny-tim's comments: The relative velocity certainly changes: You start out moving toward the source and end up moving away from it.
Well lets say it was heading stright for the observer, and the observer could see both forward and behind. He is right, relativley there is no difference, the doppler effect collapses...
However, in both cases the light is always heading towards the observer after being emitted from the object.
So? The light/sound always moves toward the observer (relatively) otherwise you won't see/hear anything. What matters for the Doppler effect is your velocity relative to the source. In one case you move towards the source; in the other, you move away. Big difference.
Oh ho Doc, say yours is the reference frame. The velocity of the train is as it is after it passes you
I think Doc Al and tiny tim are talking about different situations. tiny tim is talking about a situation where the motion of the source of sound is slightly off to one side of the observer, the velocity is continuously changing so the frequency heard is continuously changing. That is also my interpretation of the original question. If the source is moving directly toward the observer, the frequency is constant (above that of the emitted signal) until the source passes then suddenly drops below the frequency of the emitted signal. That is the situation Doc Al is referring to. Note that in the first case, while the change in frequency is continuous, it is not linear. There will be relatively little change in the frequency when the source is farther off, most change when the source is nearest. That effect increases when the point of "closest approach" to the observer is closer to the observer- that is when the source just misses the observer.
In this context, "relative velocity" refers to the radial component of the rate of change of the position vector of the source with respect to you (the observer). As the source approaches, the length of that vector is decreasing; as the source recedes, its length increases.
Wait a minute, with light it doesnt matter what your relative velocity is, light is only one speed c, invariant. So... If you had a light emitting diode travelling to you, then away from you, whats the difference? The light is traveling at speed c to you at all times. Next time I get pulled over I know what my argument is going to be. "Its only a 4 cylinder" isnt working anymore.
Again, it's the speed of the source that matters, not the speed of the light. Same thing with sound: In still air, the speed of sound with respect to a stationary observer will be the same, regardless of the speed of the source. (In fact, that was the example that started this thread.)
I was not aware of any difference between relative motion when the source of sound is slightly off to one side of the observer and when they are not. What is the cause for this difference? What I originally meant to say is that the observed frequency continuously changes even when the source and observer are moving toward eachother,and separately when they are moving away from eachother,and also that at the point of closest approach,the observed frequency equals the real frequency. Doc Al said that the observed frequency changes only when the relative motion changes from 'moving toward' to 'moving away'---that's understandable,but I came accross a source which said that the observed frequency changes continuously during the interval that the source and observer move toward eachother and also during the interval that they move away from eachother. This is what I don't understand--on these individual intervals,there is no change in relative velocity of 'moving toward' or 'moving away'. Again at the point of closest approach,there is still relative motion between source and observer,so shouldn't there be a different observed freqeuncy even here? This seems to confirm that the observed frequency does indeed change continuously during the 'moving towards eachother' part and then separately on the 'moving away from eachother' part,and that the observed frequency is in some way related to the 'distance between the source and observer. I really don't understand it!!
Is this the same thing that I found on the wesite that said 'the observed frequency of an approaching object declines monotonically from a value above the emitted frequency, through a value equal to the emitted frequency when the object is closest to the observer, and to values increasingly below the emitted frequency as the object recedes from the observer'??
The doppler effect as you think holds in the ideal condition that the relative velocity is the same throughout, but in real cases it becomes a monotonically decreasing curve. The doppler effect would be as you thought if you stood on linear track of an approaching train with constant velocity and the train went through you, but you stand by the side and the component of velocity vector towards you goes on decreasing and becomes zero when closest to you and agin goes on increasing like the velocity vector of a parabolic curve when a ball is thrown up, if you were to see it facing perpendicular to the earth in the air at the point of 0 velocity. The formulae still hold true but there is change in frequency as there is change in velocity.
If the source is moving directly towards you, then the observed frequency is shifted but steady; similarly, if the source moves directly away from you. In such a case the observed frequency doesn't continually change. Of course, that situation is unrealistic. Usually, the source doesn't come directly at you, otherwise you'll be hit. It passes by you. If you imagine a line drawn from you to the source, the length of that line--which represents the distance between the source and observer--changes as the source approaches you (at an angle), passes by you, and then recedes from you. The rate of change of that distance is the "relative velocity" that we are concerned with. That rate of change varies continuously as the source moves. The only relative motion that counts (for the non-relativistic Doppler effect, at least) is motion toward or away from the observer. At the point of closest approach the source is moving sideways with respect to the observer, thus the radial velocity (the rate of change of the distance between source and observer) is momentarily zero. At that moment the source is neither getting closer or farther from the observer.
I suppose that when the source and observer are in the process of moving past eachother,starting from a certain distance,there must be some component of the relative velocity which is continuously changing,resulting to the continuously changing observed frequency.Which component is that? I'll probably understand this better,if I know exactly how a particular component of the relative velocity changes continuously.
I suppose to track the continuously changing observed frequency,one would have to apply the same formulae separately for every instant of the motion,right?