Sine wave relationship with physical waves

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DLF4196
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This is probably pretty basic but I've never actually seen an explanation of how exactly the sine wave relates to the physical waves it is so commonly used to represent. Could it be imagined as like the periodic thumping of a speaker where the peak of the sine graph represents maximum air compression and trough maximum rarefaction? I used to imagine it being the actual shape of the wave but clearly that isn't the case because, as I understand it, waves don't actually look like squiggly lines propagating through space. Thanks in advance for any help!
 
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Yes you're right about the speaker, since sound waves are longitudinal so do not resemble sine waves. However, other waves such as electromagnetic waves and water waves* are transverse, so they do look more like sine waves propagating through space (of course, you can't directly observe an EM wave). It's very unlikely in nature that you'd get a wave exactly resembling sin(x), but when writing the equation of a wave we can introduce the wavenumber, ##k##, and the angular frequency, ##\omega##, to alter the shape of the sine wave so that it resembles the physical wave, the equation being ##y=sin(kx-\omega t)## in two dimensions.

*water waves can actually be longitudinal and transverse simultaneously - the individual molecules follow elliptical paths along the direction of wave propagation.
 
If you strike a tuning fork, the sound wave is, as sk1105 pointed out, longitudinal so not a sine wave but its density profile IS a sine wave. Were it not so, the sound reaching your ear would not be a pure musical note.

Electrical waves generated by a rotating generator will be sine waves.
 
Ok that makes more sense, thank y'all so much!
 
Another quick question if y'all don't mind. When you're using a slinky to model an S-wave, why, when you push down in order to start the wave moving, does the section in front of that downward pulse move upward? I guess, more what I'm getting at is what is the mechanism of energy transfer that causes the particles in front of the downward pulse to move up above their original position instead of just remaining at the original level? Hopefully that question makes a little bit of sense. Thanks in advance!
 
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I think you are most likely making an upward movement as part of your initial motion even though you don't think you are, OR you are giving a slight forward push to the rope (or whatever it is)
 
DLF4196 said:
This is probably pretty basic but I've never actually seen an explanation of how exactly the sine wave relates to the physical waves it is so commonly used to represent. Could it be imagined as like the periodic thumping of a speaker where the peak of the sine graph represents maximum air compression and trough maximum rarefaction? I used to imagine it being the actual shape of the wave but clearly that isn't the case because, as I understand it, waves don't actually look like squiggly lines propagating through space. Thanks in advance for any help!
Most waves in nature are not Sine Waves. They can often be analysed as the sum of a set of sine waves but that's really just a bit of convenient Maths which allows us to study a wave, either as a varying pressure, displacement, voltage etc in time or in terms of its spectrum.
When you see a speaker "thumping" that will be at the rate of the beats in the music and not, probably, at the frequency of even the lowest instrumental note involved. If you plotted that movement against time on a graph, you would get a sequence of 'smoothed' pulses at say 120 per minute but not a sine wave.
The nearest thing we can 'see' to a sine wave is probably a low amplitude surface wave on water (i.e. waves offshore). In fact even they are not sinusoidal and are a combination of longitudinal and transverse - but they do tend to be uniform and continuous over a long stretch. They get decidedly 'peaky' in shallow water and non-sinusoidal looking.