Question

Amplitude of a travelling wave on a string is 1mm. If linear mass density of string is ${10}^{-4}kg$ $m^{-1}$ , tension in the string is $1N$ and frequency of vibration is $10Hz$, then average power needed to maintain such waves in string is : (${\pi }^2=10$)

• A. $3\times {10}^{-5}W$
• B. $2\times {10}^{-5}W$
• C. $4\times {10}^{-5}W$
• D. ${10}^{-5}W$

Answer 1

Answer: (B)

$2\times {10}^{-5}W$

$P{}_{av}=\frac{\mu {\omega }^2{A}^{2}V}{2}=\frac{{10}^{-4}\times 4{\pi }^2\times {10}^2\times {10}^{{}^{-6}}\times \sqrt{{10}^4}}{2}$
$=2{\pi }^2\times {10}^{-6}$
$=2\times {10}^{-5}W$