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Sorry if this post is a bit wordy but I've been going round in circles and I thought I'd see if anyone on here can help, it's also my first post so be nice...

I've been trying to understand how Newton miscalculated the speed of sound. I know that he thought that the propagation of a sound wave was an isothermal process and he worked out the speed based on air's elasticity and density. I'm also aware that it is actually an adiabatic process. I understand this to the point that there is a local change in temperature due to the compression and rarefaction half - cycles of the waveform and that the these changes occur so quickly that no heat can enter or leave the cycle, hence an adiabatic process. What I don't understand is why this heating and cooling cause the speed of sound to increase? I have a few ideas but I haven't been able to find an explanation anywhere and am beginning to think this because the answer is so obvious it doesn't need saying!!! Any help with this will be greatly appreciated.

Thanks

Justin