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Homework Statement
A 1.2 m tube is closed at one end. A stretched wire is placed near the open end. The wire is
0.330 m long and has a mass of 9.6 g. 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 that column’s
fundamental frequency. Find (a) that frequency and (b) the tension in the wire.
I only have a problem finding the frequency since the wave speed is not given. Because both the wire and the air are oscillating at their fundamental frequency there must be a way to use this to find the frequency without the wave speed.
Homework Equations
kdx/dt -w = 0 => dx/dt = w/k = f λ => v = f λ => f = v/λ
3. The Attempt at a Solution
λstring = 2Lstring
λair = 4Ltube
fstring = fair
vstring/λstring = vair/λair => vstring/2Lstring = vair/4Ltube => vair = 7.42vstring