Longitudinal Waves - are they very different?

[Stealth849]

Homework Statement

A continuous sinusoidal longitudinal wave is sent along a coil spring from a vibrating source attached to it. The frequency of the source is 25vib/sec, and the distance between successive rarefactions in the spring is 24cm.

a) Find the wave speed

b) if the max longitudinal displacement of a particle in the spring is 3.0cm, and the wave moves in the -x direction, write the equation for the wave. Let the source be at x = 0, and displacement at x = 0 and t = 0 be zero.

Homework Equations

v = λf

k = 2∏/λ

ω = 2∏f

D(x,t) = Asin(kx - ωt)

The Attempt at a Solution

Just looking for some clarification on everything here - the fact that it is a longitudinal wave kind of freaks me out a bit, but it should be able to be modeled the same as a transverse wave right?

v = λf = 0.24*25 = 6m/s

then to model the wave...

Amplitude should be the maximum displacement of a particle, 0.03m

k = 2∏/λ = 2∏/0.24
ω = 2∏f = 50∏

D(x,t) = Asin(kx+ωt) = 0.03sin(2∏x/0.24 + 50∏t)

Is this equation correct for this longitudinal wave?
Thanks

 

[haruspex]

Yes, that all looks correct. (Sound waves are longitudinal too, as are pressure waves in solids.)