Finding displacement amplitude given frequency and pressure

AI Thread Summary
The discussion revolves around calculating the displacement amplitude of a sound wave with a frequency of 160 Hz and a pressure amplitude of 29 Pa in air at 20 °C. The relevant equations include the relationship between pressure amplitude, displacement amplitude, and wave properties. An initial calculation yielded a displacement amplitude of 4.44 x 10^-4 m, which was deemed incorrect. Participants pointed out that the wave number k should be calculated as 2π/λ, and clarified that k is related to frequency and wave speed through the equation λf = Vs. The conversation emphasizes the importance of using the correct formulas for accurate results in sound wave calculations.
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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?
 
Physics news on Phys.org
k=f/Vs is not accurate, since k is 2π/λ

λf = Vs

ω/k = Vs
 

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