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Wave intensity2/21/2023 ![]() ![]() So then I've got power divided by area times the area that I'm absorbing and it all makes perfect sense. So if I want to know how much power I'm absorbing from the sound wave then what I'm going to do is I'm going to take the area of my ear and multiply by the intensity of the sound wave. Intensity is power per unit area, so we can see here that a sound wave coming I'm only going to get a little bit of it. So what I'm really interested in is what part of that power I'm I really absorbing, so what this is associated with is something called intensity. But I'm not hearing all 100 watts, I'm surrounding the speaker taking all the energy, right I'm only hearing part of it. Now that's measured in watts, 1 watt is 1 joule per second and of course we're all used to that from power.Īlright so that's all fine and good but let's say that I've got a sound source here and it's got a power of 100 watts alright so it's sending out these sound waves. So it's the rate of energy flow, the power change in energy over change in time. So what we really ought is ask about how much power is being carried, how much energy divided by time. But with a periodic wave we keep on getting assaulted again and again and again so it doesn't really make sense to talk about how much energy is carried because it keeps on increasing as the wave keeps on coming. So that indicates to us that energy should be proportional to the square of the amplitude of a wave. The energy of a mass in simple harmonic motion is equal to one half times spring constant times the square of the amplitude. So first off the energy carried by a wave can be considered analogous to the energy carried in simple harmonic motion. ![]() ![]() Now it's not a direct correlation so let's kind of go through this. As promised, the intensity is proportional to the square of the electric field.Let's talk about wave intensity intensity is a word that we use to describe how much energy is associated with a periodic wave. Where is the amplitude of the electric field of the plane wave. In terms of the phasor electromagnetic fields, we can write the time-average intensity as The averaging will wipe out the term oscillating at double frequency, leaving behind the DC term. Your eye and many optical detection devices can’t detect the rapidly oscillating term in the instantaneous intensity, but instead detect the intensity averaged over many cycles of oscillation (time-averaged intensity). As a reminder, optical frequencies are on the order of. You can see there’s one non-fluctuating term and one term fluctuating at twice the optical frequency. Using the cosine double-angle formula, this equals. Therefore, the instantaneous intensity will oscillate in time as. For time-harmonic propagating waves, both and will each oscillate in time as. The magnitude of the Poynting vector is the instantaneous intensity. The direction of the Poynting vector is the direction of the power flow, which for the plane waves we’ve written will be the same as the direction of propagation. If we have the electromagnetic wave fields and, we can calculate the intensity from the Poynting vector, There is some lack of uniformity in the usage of terminology in optics, but the power per area is commonly referred to as the intensity ( ). We are generally interested in the optical power per unit area of a light beam, as illustrated below:Īs you might imagine, a modest amount of optical power illuminating a very small area can cause significant damage. ![]()
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