Question

A transverse wave $y=5\sin (3t-x)$, where $y,x,t$ are in SI units, is propagating on a stretched string having density $\rho =1{\text{kg/m}}^3$. Find the intensity of the propagating wave.

• A. $200{\text{W/m}}^2$
• B. $300{\text{W/m}}^2$
• C. $325{\text{W/m}}^2$
• D. $337.5{\text{W/m}}^2$

Answer 1

The correct option is D $337.5{\text{W/m}}^2$

Equation of wave is given by
$y=5\sin (3t-x)$
$\Rightarrow$ Amplitude $\left(A\right)=5\text{m}$ and $\omega =3\text{rad/s};k=1{\text{m}}^{-1}$
Also,
wave velocity $\left(v\right)=\frac{\omega }{k}=3\text{m/s}$
We know
Intensity of the wave is $\left(I\right)=\frac{1}{2}\left(\rho v\right){\omega }^2{A}^2=\frac{1}{2}(3\times 1)3^2\times 5^2=337.5{\text{W/m}}^2$