A 36 cm long sonometer wire vibrates with frequency of 280 Hz in fundamental mode, when it is under tension of 24.5 N. Calculate linear density of the material of wire.

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#### Solution

Given:

l = 0.36m

T = 24.5N

n = 280Hz

To find:

m = ?

Formula:

n = `1/(2l) sqrt(T/m)`

Solution:

n = `1/(2l) sqrt(T/m)`

`2ln = sqrt(T/m)`

`4l^2n^2 = T/m`

`m = T/(4l^2n^2)`

m = 24.5/(4 × 0.36^{2} × 280^{2})

m = 24.5/40642.56

m = 6.028 × 10^{-4} kg/m

Concept: Applications of Gauss’s Law

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