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Baritone
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Homework Statement
Suppose a tube is filled with helium gas at a pressure of 0.11MPa and a temperature of 297K. If a piston of area of 400mm2 at one end of the tube creates sound by moving sinusoidally with a frequency of 60Hz, creating a wave with amplitude of 3.8mm,
what power goes into (I'm assuming he means either max power or average power, but honestly I'm not sure what he meant by "power goes into") the sound waves formed?
T = 297k
P(initial) = 0.11MPa = 1.1×105Pa
ƒ = 60Hz
A = 3.8mm = 0.0038m
Homework Equations
PV = nRT, ρ = PM / RT, β = v2ρ, POWER(max) = √(μF) ⋅ω2A, ω = 2(pi)⋅ƒ, v2 = F / μ, PRESSURE = F / (AREA), μ = ρV / L= ρr2(pi) --->
*because V = Lr2(pi), ω = kv, kλ = 2(pi)
The Attempt at a Solution
I got ρ = 0.1782 (approx) . I've been struggling a lot with this problem even though I don't have much work here to show for it. Most of the couple hours (literally hours) I've spent staring at this problem has been spent scouring the book for various equations that look like they may possibly help. I just can't figure out how to get the velocity (v) or the k without being given one of the two. Also I apologize for having to type in pi. I couldn't find the symbol in the available options and I don't see it on my keyboard. I also did some simple conversions from mm to meters, and so on.