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Question
A sitar wire is replaced by another wire of same length and material but of three times the earlier radius. If the tension in the wire remains the same, by what factor will the frequency change?
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Solution
Frequency of vibrations produced by a stretched wire
`v = n/(2l) sqrt(T/n)`
Mass per unit length μ = `"Mass"/"Length"`
= `(pir^2 lp)/l`
= `pir^2p` ......[∵ M = vp = Alρ = πr2lρ]
∴ `v = n/(2l) sqrt(T/(pir^2ρ)`
⇒ `v ∝ sqrt(1/r^2)`
`v ∝ 1/r`
Hence, when the radius is tripled, v will be `1/3` rd of the previous value.
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