Why is that we draw a longitudinal wave like a transverse wave?
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|dw:1333035994637:dw| how does this show a longitudinal wave?
the diagramme shows the value of distanse from rest point |dw:1333038571923:dw|
I think you are asking - Why do we have a sinusoidal graph of a wave that has particles vibrating longitudnally ? See, the sinusoidal graph is a displacement, Y Vs. Time, t graph. The general equation of such graphs are of the form \[Y = Ymax. \cos (\omega.x - Kt )\]
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As mos1635 says, the sine form representation is not a picture of the wave. It shows the variation of the displacement of the wave with respect to time. It is a consequence of the fact that waves are simple harmonic motions, and thus can be represented by harmonic functions(sine or cosine).
Both latitudinal and longitudinal wave functions can be represented thus. But it does not give the 'picture' of the wave(Though for waves on a string, it co-incidentally does). Similarly the displacement-time graph of a particle does not show the actual path taken by a particle. It shows the relationship between distance covered and time taken, and how that relationship varies with time.