Definition of Intensity of a wave: In a medium, the energy per unit area per unit time delivered perpendicuar to the direction of the wave propagation s caled the intensity of the wave. It is denoted by $I$. If the energy $E$ is delivered in the time $t$ rom area $A$ perpendicular to the wave propagation, then $I=\frac{E}{At} \qquad{1}$ Unit: $Joule/m^{2}-sec$ or $watt/m^{2}$ Dimensional formula: $[MT^{-3}]$ We know that the total mechanical energy of a vibrating particle is $E=\frac{1}{2}m \omega^{2} a^{2}$ Where $\omega$ is the angular frequency and $a$ is the amplitude of the wave. $E=\frac{1}{2}m (2\pi n)^{2} a^{2} \qquad \left( \omega=2\pi n \right)$ $E=2 \pi^{2} m n^{2} a^{2} \qquad(2)$ Where $m$ is the mass of the vibrating particle. Now substitute the value of $E$ from equation $(2)$ to equation $(1)$. So the intensity of the wave $I=\frac{2 \pi^{2} m n^{2} a^{2}}{At} \qquad(3)$ If the wave travels the distance $x$ in time $t$ with v
(The Advance Learning Institute of Physics and Technology)