A variable length air column (closed on one end) is placed just below a vibrating wire of mass 5.00g, which is fixed at both ends. The length of the air column is gradually increased from zero until the first position of resonance (first harmonic) is observed at 34 cm. The wire is 120 cm long and is vibrating in its third harmonic. If the speed of sound in air is 340 m/s, what is the tension in the wire?

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Chapter1: Units, Trigonometry. And Vectors
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A variable length air column (closed on one end) is placed just below a vibrating wire
of mass 5.00g, which is fixed at both ends. The length of the air column is gradually
increased from zero until the first position of resonance (first harmonic) is observed at 34
cm. The wire is 120 cm long and is vibrating in its third harmonic. If the speed of sound
in air is 340 m/s, what is the tension in the wire?

Expert Solution
Step 1

For a closed end air column, the 1st harmonic frequency is given as,

Physics homework question answer, step 1, image 1

Here, v is the speed of sound in air and L is the length of the closed-end air.

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