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Question
A sonometer wire of length 0.5 m is stretched by a weight of 5 kg. The fundamental frequency of vibration is 100 Hz. Calculate the linear density of wire.
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Solution
Data: L = 0.5 m, T = 5 kg = 5 x 9.8 = 49 N,
n = 100 Hz
n = `1/(2"L")sqrt("T"/"m")`
∴ Linear density, m = `"T"/(4"L"^2"n"^2)`
= `49/(4(0.5)^2(100)^2`
= 4.9 × 10−3 kg/m
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