Why did Author Use Cosine/Sine for Periodic Sound Waves?

[jwxie]

Homework Statement

I am confused with why the author uses this form for periodic sound waves.

If s(x,t) is the position of a small element relative to is equilibrium position, we can express this harmonic position function as \[s(x,t) = s_{max}cos(kx-wt)\]

Why did he use cosine instead?
Later, he states

The variation in the gas pressure \Delta P\] measured from the equilibrium value is also periodic. For the position function desribed above (in this thread), \Delta P\] is given by

\[\Delta P = \Delta P_{max}sin(kx-wt)\]

Note he uses sin this time.

I know that the difference between sine and cosine is the phase offset, by 90 degrees.

But why did the author uses cosine for the first equation, and use sine in the second?

There must be a reason for this. He has been consistent with sin convention with traveling waves (previous chapter).

---edited----
For the second equation I understood now that it was derived using the first equation, and thus taking the partial s / partial x we get sine instead. So why did he use cos in the beginning, anyway?

I also understand that sound waves is longitudinal wave.

Thank you!

 

[Delphi51]

It is a little confusing, but it really doesn't matter whether you use sine or cosine - just a matter of where on the wave you choose x=0 and t=0. Perhaps the author wanted to end up with sine for the pressure wave so he started with cosine for the displacement to achieve that end.