Question

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

Answer 1

Explanation:

the answer is m= 6.028 × 10^-4

Answer 2

The linear density of the material of the wire is $6.0\times10^-^4kg/m$.

Explanation:

Fundamental frequency of a wire is given as

$f=\frac{1}{2L} \sqrt{\frac{T}{m} }$

The linear mass density of the wire,

$m=\frac{T}{4L^2f^2}$

Here T is the tension in the wire, L is the length of the wire and f is the frequency of the wire.

Given T = 24 .5 N, L = 36 cm = 0.36 m and f = 280 Hz.

Substitute the given values, we get

 $m=\frac{24.5N}{4\times(0.36m)^2\times(280Hz)^2}$

$m =0.000602kg/m=6.0\times10^-^4kg/m$

Thus, linear density of the material of the wire is $6.0\times10^-^4kg/m$

#Learn More: Linear Mass density.

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