Question

A stretched string is forced to transmit transverse waves by means of an oscillator coupled to one end. The string has a diameter of 4mm. The amplitude of the oscillation is ${10}^{-4}m$ and the frequency is 10 Hz. Tension in the string is 100 N and mass density of wire is $4.2\times {10}^{3}kg/m^3$ ​. Find Average energy flow per unit time

• A. $4.5\times {10}^{-5}J/s$
• B. $5.5\times {10}^{-5}J/s$
• C. $6.5\times {10}^{-5}J/s$
• D. $7.5\times {10}^{-5}J/s$

Answer 1

The correct option is A

$4.5\times {10}^{-5}J/s$

Average energy flow per unit time is the power transmitted,

P = Power

$=\left(\frac{1}{2}\rho {\omega }^2{A}^2\right)\left(sv\right)=\left(u\right)\left(sv\right)$

Substituting the values, we have

$P=(8.29\times {10}^{-2})\left(\frac{\pi }{4}\right){(4.0\times {10}^{-3})}^2\left(43.53\right)=4.53\times {10}^{-5}J/s$

Power required to drive the oscillator is obviously $4.53\times {10}^{-5}J/s$