Question

A wire of linear density is 8×10^_3 kg/m and length 2m is stretched by a weight of 20kg the fundamental frequency of vibration of the wire is wire is answe​

Answer 1

Given:

A wire of linear density is 8×10^_3 kg/m and length 2m is stretched by a weight of 20kg.

To find:

Value of fundamental frequency?

Calculation:

• First see the diagram !

$\sf \dfrac{ \lambda}{2} = l$

$\sf \implies\lambda = 2l$

Now, fundamental frequency is :

$\sf \: f = \dfrac{v}{ \lambda}$

$\sf \implies\: f = \dfrac{ \sqrt{ \dfrac{T}{ \mu} } }{ \lambda}$

• 'T' is tension and $'\mu'$ is linear mass density.

$\sf \implies\: f = \dfrac{ \sqrt{ \dfrac{mg}{ \mu} } }{ \lambda}$

$\sf \implies\: f = \dfrac{ \sqrt{ \dfrac{20 \times 10}{8 \times {10}^{ - 3} } } }{2l}$

$\sf \implies\: f = \dfrac{ \sqrt{ \dfrac{20 \times 10}{8 \times {10}^{ - 3} } } }{2 \times 2}$

$\sf \implies\: f = \dfrac{1.58 \times {10}^{2} }{2 \times 2}$

$\sf \implies\: f = 39.5 \: hz$

So, fundamental frequency is 39.5 Hz