A tube of length L is closed at one end. A stretched wire is placed near the ope

Question

A tube of length L is closed at one end. A stretched wire is placed near the open end. The wire has a length l and has mass m. It is fixed at both ends and oscillates in its fundamental mode. By resonance, it sets the air column in the tube into oscillation at the column's fundamental frequency. Find that frequency and the tension in the wire. (Use any variable or symbol stated above along with the following as necessary: vs for the speed of sound.)
f = Your answer is correct.
t = Your answer is incorrect.

Explanation / Answer

Resonant pipe fundamental wavelength lambda = 4L, fundamental frequency f = c/lambda
B. Since I don't know the intended value for c, I can't give a numeric answer. However from the basic equation f = sqrt(T/(m/L))/(2L) you can solve for tension T.
T = 4f^2*mL (L here is the length of the wire). See the ref.

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