Question

A transverse sinusoidal wave is generated at one end of a long horizontal string by a bar that moves with an amplitude of $1.12cm$. The motion of the bar is continuous and is repeated regularly $120$ times per second. The string has linear density of $117g/m$. The other end of the string is attached to a mass $4.68kg$. 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 :

• A. 10.884 m / s
• B. 8.44 m / s
• C. 844 m / s
• D. None of these

Answer 1

Answer: (B)

Tension in the string should be

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