Finding displacement amplitude given frequency and pressure

[leinad0213]

Homework Statement

What is the displacement amplitude of a sound wave of frequency 160.0 Hz in air at 20 °C at the pain-threshold pressure amplitude of 29.0 Pa?

f = 160 Hz
Vs = 343 m/s
ΔP = 29 Pa

Homework Equations

ΔP(x,t) = (ΔP)cos(kx - wt) = β*s*k*cos(kx - wt)
k = f/Vs

The Attempt at a Solution

ΔP = βsk

Therefore, s = ΔP/(β*k) = (ΔP*Vs)/(f*β)

β = 1.4 * 10^5 Pa

So the answer I got was 4.44*10^-4 m which is wrong. Am I missing something here?

 

[Liquidxlax]

k=f/Vs is not accurate, since k is 2π/λ

λf = Vs

ω/k = Vs