Question

The length of the wire shown in figure between the pulleys is 1.5 m and its mass is 12.0 g. The frequency of vibration with which the wire vibrates in two loops leaving the middle point of the wire between the pulleys at rest is

• A. 10 Hz
• B. 30 Hz
• C. 40 Hz
• D. 70 Hz

Answer 1

The correct option is D 70 Hz

Given:

$l$ = 1.5 m , mass = 12 g

Mass of unit length = $\frac{12}{1.5}=8\times {10}^{-3}kg/m$

$T=9\times g=90N$

$\lambda =1.5m$,

$f=\frac{1}{l}\sqrt{\frac{T}{\mu }}=\frac{1}{1\cdot 5}\sqrt{\frac{90000\times 1\cdot 5}{12}}$
$=70Hz$