doppler effect TBR

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Oh_Gee

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so in TBR, it says

fL=(v/v-vs)fS
Equation (6.5) is telling us that the source of the sound moves towards you (i.e., vs > 0), then you hear a higher pitch (corresponding to a greater frequency). If the source of the sound moves away from you (i.e., vs < 0), then you hear a lower pitch (corresponding to a smaller frequency).

which makes sense to me because if vs gets bigger, then the denominator gets smaller which means fL will be bigger

but then on the next page it says

vs Speed of the source relative to still air
vs is negative (-), if the source is moving towards the listener.
vs is positive (+), if the source is moving away from the listener.

so is vs supposed to be + or - when the source is moving towards the listener? because if vs is - when the source is moving towards the listener, then won't the denominator get bigger, leading to a bigger fL?

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I just remember it as what it would feel like in real life. If the vs is in the denominator, I would want the entire denominator to get SMALLER if the thing is approaching (thinking of a train coming near me ...). So, I would just plug in "vs" to make the whole thing smaller (i.e. subtract) -- I didn't really worry about memorizing signs.

fL is supposed to increase if the source is coming toward you ...
 
so in TBR, it says

fL=(v/v-vs)fS
Equation (6.5) is telling us that the source of the sound moves towards you (i.e., vs > 0), then you hear a higher pitch (corresponding to a greater frequency). If the source of the sound moves away from you (i.e., vs < 0), then you hear a lower pitch (corresponding to a smaller frequency).

which makes sense to me because if vs gets bigger, then the denominator gets smaller which means fL will be bigger

but then on the next page it says

vs Speed of the source relative to still air
vs is negative (-), if the source is moving towards the listener.
vs is positive (+), if the source is moving away from the listener.

so is vs supposed to be + or - when the source is moving towards the listener? because if vs is - when the source is moving towards the listener, then won't the denominator get bigger, leading to a bigger fL?




Yes, you seemed to have figured it out, but to reassure you...

The equation is actually:


fL=[v/ (v +/- vs)] fS

The difference being that the sign value is intrinisically changing depending on the direction of the sound source - the equation is not normally -, but either + or - depending on the direction. Otherwise, it would be problematic if the equation was normally v-vs in the denominator because, for example, if the source was moving towards you (i.e. -vs) it would make the denominator v- (-vs) or v+vs resulting in a smaller fL and we know from real experiences that this is not the case.

The sign will change when you know the direction. Is the sound/source is moving towards the listener, the denominator is v - vs creating a smaller denominator leading to a larger fraction and a greater fL.

Contrarily, if the sound/source is moving away from the listener, the denominator will be v + vs creating a larger denominator leading to a smaller fraction and a smaller fL.

Hope this helps some!
 
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