Physics problem? Sound and waves?

Question

A 29.0cm -long wire with a linear density of 30.0g/m passes across the open end of an 88.0cm -long open-closed tube of air. If the wire, which is fixed at both ends, vibrates at its fundamental frequency, the sound wave it generates excites the second vibrational mode of the tube of air. What is the tension in the wire?

JullyWum · Accepted Answer

2nd vibration (resonance) occurs when tube length L = 3λ/4 
Wavelength λ = 4 x 0.88m / 3 = 1.17m
Frequency = vel of sound in air / λ .. .. 340m/s / 1.17m .. .. f = 291 Hz

The frequency of the wire driving the vibrations in the tube = 291 Hz

Resonant frequency for wire .. f = (1/2L) √(T/μ)
f² = (1/4L²)(T/μ)

T = f² 4L²μ .. ..291² x 4 x (0.29m)² x 0.030kg/m .. .. ►T = 854.60 N

Physics problem? Sound and waves?

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