Question

A string of length 0.5 m and linear density 0.0001 Kg m-1 kept under a tension 1 N. Find first three overtones (n>1 harmonic) of the string when it is plucked at mid points.​

Answer 1

Explanation:

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Answer 2

Given:

l=0.5m

linear density 0.0001 Kg

T=1 N

$V=\sqrt{\frac{I}{\mu}}$

$v=\sqrt{\frac{1}{0.0001}}\\v=100 \mathrm{~m} / \mathrm{s}$

$\text { 1st overtone }=2\left[\frac{v}{2 l}\right]$

$\frac{2 \times 100}{2 \times 0.5}$

$=\frac{1000}{5}$

=200

$2^{\text {nd }} \text { overione }=3\left[\frac{V}{2 l}\right]$

$=\frac{3 \times 100}{2 \times 0.5}$

=300

$3^{\text {rd }} \text { overtone }=4\left[\frac{v}{2 \ell}\right]$

$=\frac{4 \times 100}{2 \times 0.5}$

=400