Question

Find the fundamental frequency of a wire of length 50 cm, diameter 0.04 cm and density 9.8 gm/cm3

under a

tension of 0.314 kg wt.​

Answer 1

Given that,

Length = 50 cm

Diameter = 0.04 cm

Density = 9.8 gm/cm

Tension $T= 0.314\times9.8\ N$

$T=3.0\ N$

We need to calculate the fundamental frequency

Using formula of frequency

$n=\dfrac{1}{2l}\sqrt{\dfrac{T}{\mu}}$

Where, l = length

T = tension

$\mu$ = linear density of wire

Put the value into the formula

$n=\dfrac{1}{2\times50\times10^{-2}}\sqrt{\dfrac{3}{9.8\times10^{-3}}}$

$n=17.4\ Hz$

Hence, The fundamental frequency is 17.4 Hz.