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(II) A sinusoidal wave traveling on a string in the negative $x$ direction has amplitude $1.00 \mathrm{cm},$ wavelength $3.00 \mathrm{cm},$ and frequency 245 $\mathrm{Hz}$ . At $t=0,$ the particle of string at $x=0$ is displaced a distance $D=0.80 \mathrm{cm}$ above the origin and is moving upward. (a) Sketch the shape of the wave at $t=0$ and (b) determine the function of $x$ and $t$ that describes the wave.

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a) $D(x, 0)=(1.00 cm) \sin \left[\left(\frac{2 \pi}{3.00 cm}\right) x+0.93\right]$b) $D(x, t)=(1.00 cm) \sin \left[\left(2.09 cm^{-1}\right) x+(1540 rad / s) t+0.93\right]$

Physics 101 Mechanics

Physics 102 Electricity and Magnetism

Chapter 15

Wave Motion

Periodic Motion

Mechanical Waves

Electromagnetic Waves

University of Michigan - Ann Arbor

Simon Fraser University

Hope College

University of Winnipeg

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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In this question, we have a lot a wave that is troubling in the string in the negative x direction and it has an amplitude of 1 centimeter. It has a couple of it has a couple of parameters. So, let's, let's just try to write down the expression for it. It has an amplitude of 1.00 centimeter. So this vice is in terms of centimeter. Amplitude is 1. It'S sodalite. We have x minus omega t, except that its travel is negative x direction, because this is actually plus a what plays is 3 centimeters, so lambda equals 3 centimeter amplitude equals or centimeter delta equals 3 centimeters. Okay, equals 2 pi over lambda, and this gives us what is to last 1. It says the frequency f equals 245 hurts and we do all we got equals to is that gives us what omega is so at t equals 0 point. A particle streak at x, equals 0 is displaced by a distance 0.8 centimeters. What that is saying is that d t equals 0 x, equals 0 equals 0.8 centimeters, and it's rooting upward. What that says, that is to say, is actually there is a face, differences or, and that's a way to think about this- is that it has u. It may also have an offset so it's possible that you also have something like this plus the constant, but i will assume that it a face difference. So the first see we need to do is we need to draw a diagram for the wave, so the amplitude is 1, but this point is 0.8. This is moving upward so since the with stenog to the left, this has to look something that this and the way place is 3 centimeter. Well, this is not quite the right scale, but tis distance should be roughly 3 centimeter and i think that is roughly iteas. It it is in me, can make sure this is 1 aisy. So the second part, of course, is to figure out the expression for it. We already list everything and we can now start a calculatin to pi. Over 3 centimeter equals 2 to the bolas times 2. Hunder for pipes is 1540 per second and the last 1. Is this equal, a centimeter and it also as with x 0. This is sine fine, so fine is 1 side of 0.80 equals 0.9 3 point. So finally, we have expression d equals sine there's 1 centimetre. I know it's 1, but i would just put it here just because it it carries a unit wizard problem. Actually, let me rewrite this equation was also used and seen it, because what is better practice leader, a sine of k, is 2.097 here k times x, plus omega radio times t finally, plus 0.93 and unit x is 8. Centimeter t is a second to his expression that we're trying to find.

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