# 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. - Physics

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.

#### 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 × 0.362 × 2802)

m = 24.5/40642.56

m = 6.028 × 10-4 kg/m

Concept: Applications of Gauss’s Law
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