# Sound waves and sound pressure

#### Booney

1. Homework Statement
Consider a sound wave in air of density 1.2 kg/m3. The displacement wave has the form s(x,t)=smaxcos(kx-$$\omega$$t) where k=8.79rad/m, $$\omega$$=3021.6 rad/s and smax=2.51 x 10-7m.
Calculate the sound pressure $$\Delta$$P(x,t) of this wave at x=0.282m and t=0.00137s. Answer in units of Pa.

2. Homework Equations
$$\Delta$$Pmax=$$\rho$$v$$\omega$$smax
$$\Delta$$P=$$\Delta$$Pmaxsin(kx-$$\omega$$t)

3. The Attempt at a Solution

I have a feeling I'm not using the correct equations because the equations I've found include a velocity, which isn't given, and don't include the displacement function. How do I relate the displacement function to the pressure equations?

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#### Xerxes1986

The only way I can think to solve this is by using the kinetic theory of an ideal gas to derive pressure based on average velocity. You can review this derivation at http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kinthe.html#c3". The important equation is:

$$\frac{1}{3} \frac{N}{V} m \bar{v}^2$$

You can calculate velocity from your displacement equation.

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