# Particle speed relative to frequency and pressure amplitude.

1. Jun 16, 2007

### Alpha Russ Omega

1. The problem statement, all variables and given/known data
A sound wave of frequency 1250 Hz., propagating through air at 0 degrees Celsius, has a pressure amplitude of 15.0 Pa. What is the maximum particle speed (in meters/second)?

2. Relevant equations
v = frequency x lambda = (2 x pi x frequency)(lambda / 2 x pi) = omega / k = sqrt(B/rho)

3. The attempt at a solution
I found that at the temperature of 0 degrees Celsius v = 331 m/s

I'm not sure how to tie these equations together and the maximum particle speed.

Anyone have any suggestions where to start on this one?
Any help will be appreciated.

2. Jun 16, 2007

### nrqed

The displacement wave has an equation of the form
$s(x,t) = s_{max} cos (\omega t + \phi)$

To find the maximum speed of the particle, you must calculate the transverse velocity of the particles, $\frac{\partial s}{\partial t}$ and find the maximum possible value it may have.

Next, you will need an equation relating the maximum displacement $s_{max}$ to the pressure amplitude (you must have covered that in class).

3. Jun 17, 2007

### Alpha Russ Omega

Aha! I was trying to use the wrong equations. It's figured out now. Thank you! :-)

4. Jun 24, 2007

### laurar07

How did it end up being?

Hey, I also have to complete that problem. How did u end up finding the solution? Thanks!

5. Mar 8, 2008

### mike115

Hmm, can you please explain how that equation for transverse particle speed also applies to longitudinal waves like sound?

6. Mar 8, 2008

### kdv

I should have said "longitudinal velocity" instead of transverse speed.
The formula I gave is still correct. Th elongitudinal velocity is simply the derivative of the longitudinal motion with respect to time so $$\frac{\partial s(x,t)}{\partial t}$$