Particle speed relative to frequency and pressure amplitude.

[Alpha Russ Omega]

Homework Statement

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)?

Homework Equations

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

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.

 

[nrqed]

Homework Statement

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)?

Homework Equations

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

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.

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).

 

[Alpha Russ Omega]

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

 

[laurar07]

How did it end up being?

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

 

[mike115]

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.

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

 

[kdv]

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

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 $$\frac{\partial s(x,t)}{\partial t}$$