Question

For a wave displacement amplitude is ${10}^{-}4m$,density of air 1.3 kg $m^{-}4$,velocity in air 340 $m{s}^{-}4$ are frequency is 2000 Hz.The intensity of wave is

• A. $5.3\times {10}^{-}4W{m}^{-}4$
• B. $5.3\times {10}^{4}W{m}^{-}4$
• C. $3.5\times {10}^{-}4W{m}^4$
• D. none of these

Answer 1

The correct option is D none of these

$\begin{array}{c}Fromthequestion\\ A={10}^{-8}m\\ \rho =1.3kg/m^3\\ v=340m/s\\ v=2000Hz\\ Theintensityofwaveisgivenbythefollowingrelation\\ I=\frac{1}{2}\rho A^2{\omega }^{2}c---\left(1\right)\\ \omega isangularfrequency,\omega =2\pi v\\ cisthespeedoflight\\ So,equation\left(1\right)becomes\\ I=\frac{1}{2}\times 1.3kg/m^3\times {\left({10}^{-8}m\right)}^2\times {\left(2\pi \times 2000Hz\right)}^2\times 3\times {10}^{8}m/s\\ I=3.0761W/m^2\end{array}$

Hence, the option $D$ is the correct answer.