so i'm in the 9th grade and as a homework assignment I have to teach myself about the doppler effect and write a analysis of it along with a diagram... I have watched many videos on the topic now and for the most part, i get it. There is one thing that I'm confused about though. I don't get why as the moving objects moves forward, the waves on the side it's moving to get smaller, is it just because the speed of the object, or just the motion of moving forward, or is it something else?basically im asking about what in the doppler effect allows the waves to get shorter (with higher frequency) sorry i know my question isn't well explained. thanks in advance to any answers.
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The forward motion crowds more waves into the same space; the 1st wave can only move at the speed of sound u, but in, say, 1 sec, the source moves forward by 10 m, then f # of waves are squeezed into a distance of only (u - 10), thus making their wavelength shorter by a factor of (u - 10)/u.
The same principle applies to the side it's going away from; just change the - sign to + above.
The same principle applies to the side it's going away from; just change the - sign to + above.
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From the frame of reference of the sound wave, the sound appears as a stationary wave form -- for example, draw a sinusoid on the x-axis and that's your sound signal. [It doesn't propagate in space as time proceeds because you're moving with the wave.]
if the observer is moving at the same speed as the wave (and in the same direction) then it would appear on your graph as a stationary point. since none of the peaks or troughs would pass the observer, a frequency of zero would be observed -- the observer would hear nothing.
since sound typically travels much faster than the observer, we only need to consider the case of the observer moving forward through the sinusoid that you drew. Since the distance between peaks of the sinusoid is constant, the rate at which the observer moves through the sinusoid determines the frequency that is observed; the faster the observer moves, the more frequently it encounters the next peak of the sinusoid, so the higher the frequency observed.
that's the basic physics that is going on.
so now just do your galilean transform back to the reference frame of a stationary source and moving observer and moving sound wave. as the observer moves towards the source, the faster sound wave appears to be traveling past the observer -- so the higher the frequency encountered. as the observer moves away from the source, the slower the wave appears to be moving past the observer -- so the lower the frequency encountered.
if the observer is moving at the same speed as the wave (and in the same direction) then it would appear on your graph as a stationary point. since none of the peaks or troughs would pass the observer, a frequency of zero would be observed -- the observer would hear nothing.
since sound typically travels much faster than the observer, we only need to consider the case of the observer moving forward through the sinusoid that you drew. Since the distance between peaks of the sinusoid is constant, the rate at which the observer moves through the sinusoid determines the frequency that is observed; the faster the observer moves, the more frequently it encounters the next peak of the sinusoid, so the higher the frequency observed.
that's the basic physics that is going on.
so now just do your galilean transform back to the reference frame of a stationary source and moving observer and moving sound wave. as the observer moves towards the source, the faster sound wave appears to be traveling past the observer -- so the higher the frequency encountered. as the observer moves away from the source, the slower the wave appears to be moving past the observer -- so the lower the frequency encountered.