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### 4.2 Intensity

Progressive waves are all about the transmission of energy through a medium, be it a mechanical energy, acoustic energy, electric energy and so on. We often make use of concept related to energywaves classified as progressive as opossed to stationary, if their waveform move. all waves in its natural states are progressive, stationary waves are formed by superposition of two waves. as waveforms are energy stored in the oscillation of the mediums particles, it should be understood that energy is transferred due to a progressive wave. Here, in this note we'll take a look at the notion of the Intensity. But first the definition,

Intensity: It is the average rate of energy transferred per unit area perpendicular to the diretion of the wave propagation. Or simply, it's the power transferred per unit area perpendicular to the direction of the wave propagation. It's SI unit is $Js^{-1}m^{-2}$.

As we have derived here, the relation of the energy in the simple harmonic motion as follows,
$$E=\frac{1}{2}kx^{2}$$
We can see that the energy is proportional to the amplitude of the wave motion.
$$E\propto x^{2}$$
where, $'x'$ is the amplitude of the oscillation.

Now, from the definition of the intensity, the mathematical expression is as follows,
$$I=\frac{E}{t\times A}$$
where $A$= surface area, $E$= Energy of the waves, $t$= time. Thus, we can write
$$I\propto x^{2}$$

Here's an easy to understand video,

Exercise: From the damping plot below, Find
1. Ratio of the intensity at point A to Point B
2. Ratio of the intensity at point A to Point C