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(II) Two traveling waves are described by the functions$$\begin{aligned} D_{1} &=A \sin (k x-\omega t) \\ D_{2} &=A \sin (k x+\omega t) \end{aligned}$$where $A=0.15 \mathrm{m}, k=3.5 \mathrm{m}^{-1},$ and $\omega=1.8 \mathrm{s}^{-1} .$ (a) Plot these two waves, from $x=0$ to a point $x(>0)$ that includes one full wavelength. Choose $t=1.0 \mathrm{s}$ . (b) Plot the sum of the two waves and identify the nodes and antinodes in the plot, and compare to the analytic (mathematical) representation.

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a) See graphb) See graph

Physics 101 Mechanics

Physics 102 Electricity and Magnetism

Chapter 15

Wave Motion

Periodic Motion

Mechanical Waves

Electromagnetic Waves

Cornell University

Simon Fraser University

Hope College

McMaster University

Lectures

03:40

In physics, electromagnetic radiation (EM radiation or EMR) refers to the waves (or their quanta, photons) of the electromagnetic field, propagating (radiating) through space, carrying electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) light, ultraviolet, X-rays, and gamma rays. Electromagnetic waves of different frequency are called by different names since they have different sources and effects on matter. In order of increasing frequency and decreasing wavelength these are: radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays and gamma rays.

10:59

In physics, Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. They underpin all electric, optical and radio such electromagnetic technologies as power generation, electric motors, wireless communication, cameras, televisions, computers, and radar. Maxwell's equations describe how electric and magnetic fields are generated by charges, currents, and changes of these fields. The equations have two major variants. The microscopic Maxwell equations have universal applicability but are unwieldy for common calculations. They relate the electric and magnetic fields to total charge and total current, including the complicated charges and currents in materials at the atomic scale. The macroscopic Maxwell equations define two new auxiliary fields that describe the large-scale behaviour of matter without having to consider atomic scale details. The equations were published by Maxwell in his 1864 paper "A Dynamical Theory of the Electromagnetic Field". In the original paper Maxwell fully derived them from the Lorentz force law (without using the Lorentz transformation) and also from the conservation of energy and momentum.

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questions that actually requires a graphing calculator. So I'd have a calculator, too few guys, so I would just try. So just try to draw his questioning as best as I can. But this is a question that is supposed to be double is a graphing calculator. So we have given a couple numbers were given equals you're pulled by five meter. Okay, equal Super first perimeter, Um, plus or minus 1.8 t physicist E and in part A, which shows t to be one second. So, um, this would just be 1.8. So this is an expression you should put into your calculator. But we also say we won't. You have atleast one wave less so it doesn't hurt to try to find the way friends away plans is to pie over K, which is pie to pi over Super five per meter, which is around 1.8 meter. And that is, um, worthless. Sure, the graph settings. The ex graphing calculator sets the axe maximum to be at least one point paid. And the amplitude we would expect to be 0.15 and negatives open. If you have the calculator, you will see that the actual wave looks something like sis don't. So this is for D two, which is the way we use a plus side that is troubled. Inches left and for the wave with minus 20 ones that Oh, this is Steven. So if this is the one which is the way we said, um, minus side, that's traveling to the right. And we also have tea, too, which is a wave with a plus sign. Is traveling to the left and somewhere Looks like, um, something like this. So you can see that compared to you a normal So I think a normal someone who looked like this. This is roughly it almost looks like it's shifted by, um, Round one force of the wave lis. And that is because if we inspect, if we look at this, we can see that 1.8 is around half of X. So that is to say, um, by introducing this Astra time off one second, it's almost equivalent. She moving X to the left or right by roughly 0.5 and 0.5 is roughly one force of a wave lands. So it's like, um, it's a normal sound wave except that is shifted to the left or right by a little bit more Zen. Zero point. Is there a 0.251 force of a lifeless. But anyways, that is a and we look at parties apart. We ask us to plot the sum of two ways and he identifies a note and anti night of the plot. Um, okay, so we can see that if we add some up, we work at something like their point d equals empty tubes always end up, and we have signed K X, which is stricken from Pax and co sign Omega T, which we already have is 1.8. This is the best medical expression of it, and if we applaud it, we will have simply to this larger 0.30 inactive 0.30 The witness also does not change its also 1.8. But here So, as I said, it's ah, things. It's a standing wave. A zoo, not an anti not does not move. It is it's standing. There is stationary. So the cost sign when we have t equals 1.8, it becomes simply part of the amplitude and this will be extending leave and the actual amplitude Is there a 0.3 times co sign 1.8. And as time goes by, what happens is that this amplitude my increase until it reaches zero wins 30 and then it would decrease. And this pretty much as vibrates with the same doubt. An anti note. And the question says We need to find a place off the no and anti note so we can find out using his expression actually goes and pie over. Um, okay, that gives us Cyril. 0.9 point eight is a place of the note, and the antidote is in the middle sees. So for anti note, we'll have X equals 0.45 and one point search for a 1.35 and we can see that is exactly what we get. Photographed

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