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Hi, so hopefully by now you have seen how we derive the wave equation for
the 1D transverse mechanical wave, that's the type of wave you see travelling along a string
as you wiggle it back and forth. And see also how the solution works and what features the solution tends to have
so we are going to expand that and see how can arrive at the same wave equation
for different physical phenomena that we know have the characteristics of a wave
and also the key thing to remember today is as soon as you get that wave equation
as you see the double spatial derivative equals the double temporal derivative
we will have, right away, the speed of that wave without even finding the solution, because we already solved it for our case
and then because we live in a 3D world, we will extend the wave equation in 3D and look at some property of
at least one type of solution we would have in 3D
In terms of different examples of waves
you might think of, first of all, light waves or electromagnetic waves, especially in the context of the course
so called Waves and Optics. Alas. Light as coming from a light bulb, or more fun...
as coming from a laser, because lasers are always fun. Laser light is actually easier to analyse
because they go in a definite direction and because they only have a single wavelength,
but we can talk about that more in the coming weeks when we get there
and also light come to us from all around the universe as we can see in the night sky
Legend has it that when Maxwell first discovers how electromagnetic waves describes light,
he took his girlfriend or fiancee I think at the time out to look at the night sky and
and obstensibly he said that he was the only person on Earth at that time who understands how
the light travels from the stars to their eyes
so that's how physicists tend to be romantic sometimes
alas
we can extend beyond our visible light region into other electromagnetic waves light radio waves, microwaves, infrared and
also x-rays. So lots of different examples of the electromagnetic waves
Another type of waves you may be thinking of is sound wave. Sound wave is a longitudinal kind of pressure wave
that moves along a medium, most likely air, but does not have to be
and you can talk about recording sound and producing sound, and we will have a deeper look at
the musical instruments and how they create sound as we move into the next couple weeks, actually
very fun, you can explain how instruments work
but today we are going to focus on how the wave equation comes about with different property of sound
another example, very common, would be your water waves, water coming up and down
it is actually a little more difficult with the water waves, because deep under water,
it actually works like a longitudinal pressure wave, much like the sound wave, but as you get up
toward the surface, the higher pressure water is allowed to swell up
and come down so you have a little combination of
your longitudinal and transverse
property and the top kind of swirls around in a circle as you can see here
which makes it a little diffiicult to analyse, so we would go into it. Today we will focus mainly on
deriving the wave equations for the electromagnetic waves and also for the sound waves
and then we will move onto extending our wave equation to 3D