A piston at one end of a gas filled circular tube of area s, Mechanical Engineering

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A piston at one end of a gas filled circular tube of area s

Problem -

A piston at one end of a gas filled circular tube of area S oscillates with real-valued velocity:

U_p(t) = U₁cos(ω₁t) + U₂sin(ω₂t)

Note that two oscillation frequencies are present. The other end of the tube has an anechoic termination. The piston has been oscillating in steady state long enough for any transients to die out. The gas sound speed is c and density is ρ.

a) Find the expression for the real-valued pressure anywhere in the tube.

b) Find the expressing for the mean-square pressure.

c) Find the average power W radiated down the tube.

d) What is the acoustics impedance of an anechoic termination?

e) If the tube is length L, and the piston is started from rest, how long does it take for the transients die out?

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Mechanical Engineering: A piston at one end of a gas filled circular tube of area s

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