Question

Sinusoidal waves 5.00 cm in amplitude are to be transmitted along a string having a linear mass density equal to $4.00\times {10}^{-2}kg/m$. If the source can deliver a maximum power of 90 W and the string is under a tension of 100 N, then the highest frequency at which the source can operate it, is $(take{\pi }^2=10)$

• A. 45.3 Hz
• B. 50 Hz
• C. 30 Hz
• D. 62.3 Hz

Answer 1

The correct option is C 30 Hz

$P=\frac{1}{2}\mu {\omega }^2{A}^{2}VusingV=\sqrt{\frac{T}{\mu }}P=\frac{1}{2}{\omega }^2{A}^2\sqrt{T\mu }\omega =\sqrt{\frac{2P}{A^2\sqrt{T\mu }}},f=\frac{\omega }{2\pi }=\frac{1}{2\pi }\sqrt{\frac{2P}{A^2\sqrt{T\mu }}}$
Using the given data, we get f = 30 Hz.