Question

A transverse wave of amplitude $0.5\text{mm}$ and frequency $100\text{Hz}$ is produced on a wire stretched to a tension of $100\text{N}$. If the wave speed is $100\text{m/s}$. What average power is the source transmitting to the wire?

• A. $60\text{mJ/s}$
• B. $49\text{mJ/s}$
• C. $40\text{mJ/s}$
• D. $70\text{mJ/s}$

Answer 1

The correct option is B $49\text{mJ/s}$

Given that,
$A=0.5\text{mm},f=100\text{Hz},T=100\text{N},v=100\text{m/s}$
Average Power $\left(P\right)=\frac{1}{2}{\omega }^2{A}^2\mu v$
Wave velocity $v=\sqrt{\frac{T}{\mu }}$
$\Rightarrow \mu =\frac{T}{v^2}$
So, $P_{av}=2{\pi }^2{f}^2{A}^2\left(\frac{T}{v^2}\right)v$
$=2{\pi }^2{f}^2{A}^2\frac{T}{v}$
$=2{\pi }^2(100{)}^2\times (0.5\times {10}^{-3}{)}^2\times \frac{100}{100}$
$=0.04934\text{J/s}$
$\Rightarrow P=49.34\times {10}^{-3}\approx 49\text{mJ/s}$