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
Sound Waves: Sound waves are mechanical waves in nature. They need a medium to propagate and so cannot be produced in a vacuum. They can move in all types of mediums as solid liquid or gas whether they are transparent or not. They propagate in the form of longitudinal waves. The particle of the medium vibrates along the direction of the propagation and so contraction and rarefaction are formed there. These are three-dimensional waves. These waves do not show a polarization effect. For a normal human being the audible frequency range is $20$ to $20000 Hertz$. The speed of the sound waves is more in a dense medium than in a rare medium. Light waves: light waves are electromagnetic waves in nature. They don't need any medium and so can produce and propagate in a vacuum. Their velocity in a vacuum is the maximum of value $3 \times 10^{8} m/s$ They can move in a transparent medium only. They propagate in the form of transverse waves. The electric field and