Question

A stretched string is observed to vibrate with a frequency 20 Hz in its fundamental mode when the supports are 60 cm apart. The amplitude at the antinode is 2 cm. The string length between the supports has a mass of 30 g. Calculate the speed of propagation of the wave and the tension in the string.

Answer 1

Solution :-

Since the string is vibrating in fundamental mode, frequency(ν) is given by :-

$\nu =\frac{v}{2L}$

Since L=0.6m and ν=20Hz;

$=>v=2L\nu\\\\=>v=2(0.6)(20)\\\\=>\boxed{\boxed{v=24ms^{-1}}}$

Since velocity of wave in a string is given by the expression:-

$\boxed{v=\sqrt{\frac{T}{\mu}}}$ where μ: linear mass density given by $\mu=\frac{M}{L}$

∴$T=v^2\mu\\\\=>T=(576)\frac{(0.03)}{0.6}\\\\=>\boxed{\boxed{T=28.8N}}$

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