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In discussing Doppler effect, we use the word "apparent frequency". Does it mean that the frequency of the sound is still that of the source and it is some physiological phenomenon in the listener's ears that give rise to the Doppler effect?

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Actually No. Here's a Flash simulation for Doppler effect which I found useful while googling. It really does exist and not some random appearance..! I don't know whether the term Apparent frequency is good to use or not...

We know that Sound is a form of mechanical vibration. When the source moves away from the stable observer at some noticeable speeds (relative to observer) or the observer moves away from the stable source, the frequency of sound perceived by the observer is always less than the actual frequency of the source. It could be easily imagined when you stand somewhere along the roadside and a speeding car passes by... (which is provided in Scene 1 of the simulation). For the reversal (i.e. either the observer or the source moving towards each other), it happens exactly antonymous...

One thing to notice in Doppler effect is that when the observer speeds at the speed of sound relative to the source, his detector (ear) doesn't oscillate at all. I mean, you'd probably hear Nothing...

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I would have to see the words in context, but the description "apparent frequency" seems strange to me. The frequency your ear detects is exactly what the most sophisticated scientific instrument would measure. The Doppler shift is real in that the frequency your ear detects is really the sound frequency in your frame.

I would guess "apparent frequency" means that in your frame the frequency of the source is different to the frequency measured in the rest frame of the source. So you could argue that in your frame the frequency of the source "appears" to be different. However I would argue that it doesn't just "appear" to be different, it really is different!

You'll find the same sort of confusion when you start learning special relativity. In your inertial frame an object moving at nearly the speed of light has its length contracted, that is you will measure the moving object to be shorter than someone making the same measurement in the object's rest frame. But there's nothing "apparent" about it: in your frame the object really is shorter.

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The source puts out the same frequency; the observer only perceives a different frequency because of the relative motion between them i.e. the actual frequency of the source remains unchanged and that this apparent change in frequency is due to the relative velocity between the source and the observer.

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