12.8 Stationary waves - How to determine linear density of wire

1.   A sonometer wire of length 0.5 m is stretched by a weight of 5 kg. The fundamental frequency of vibration is 100 Hz. Determine the linear density of material of wire.

Given :

Length of Wire                       =       l         =       0.5 m

Tension on Wire                    =       T       =       Mg    =       5 × 9.8 N

The Fundamental frequency =       n       =       100 Hz

Linear Density of wire            =       μ       =       ?      

Solution:

N =  1 / 2 l  √ ( T / μ )

100 =  1 / ( 2 X 0.5 ) √ ( ( 5 X 9.8 ) / μ )

100 =  1 / 1  √ ( 49 / μ )

10² = √ ( 49 / μ )

Squaring on both the sides we get,

10⁴ =  49 / μ

Therefore

μ =  49 / 10⁴

i.e.

Linear density of material of wire = μ = 0.0049 kg / m