1. Tardigrade
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  3. Physics
  4. A transverse sinusoidal wave is generated at one end of a long horizontal string by a bar that moves with an amplitude of 1.12 cm. The motion of the bar is continuous and is repeated regularly 120 times per second. The string has linear density of 117 g / m. The other end of the string is attached to a mass 4.68 kg. The string passes over a smooth pulley and the mass attached to the other end of the string hangs freely under gravity. The maximum magnitude of the transverse speed is :

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Q. A transverse sinusoidal wave is generated at one end of a long horizontal string by a bar that moves with an amplitude of $1.12\, cm$. The motion of the bar is continuous and is repeated regularly $120$ times per second. The string has linear density of $117\, g / m$. The other end of the string is attached to a mass $4.68\, kg$. The string passes over a smooth pulley and the mass attached to the other end of the string hangs freely under gravity.
The maximum magnitude of the transverse speed is :

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Solution:

Tension in the string should be
image
$T=m g$
$T=46.8\, N$
Speed of wave should be
$v=\sqrt{\frac{t}{\mu}}=\sqrt{\frac{46.8}{0.117}}=20\, ms ^{-1}$
Power of wave on string is given as
$P=\frac{1}{2} A^{2} \omega^{2} \mu v$
$=\frac{1}{2} \times\left(1.12 \times 10^{-2}\right)^{2} \times(2 \pi \times 120)^{2} \times 0.117 \times 10^{-3} \times 20$
$=0.0834\, W$