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(II) The displacement of a transverse wave traveling on a string is represented by $D_{1}=4.2 \sin (0.84 x-47 t+2.1)$ where $D_{1}$ and $x$ are in $\mathrm{cm}$ and $t$ in $s$ . $(a)$ Find an equation that represents a wave which, when traveling in the opposite direction, will produce a standing wave when added to this one. (b) What is the equation describing the standing wave?

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a) $D_{2}=4.2 \sin (0.84 x+47 t+2.1)$b) $D_{R}=2(4.2) \sin [(0.84 x+2.1)] \cos \left[\left(47 s^{-1}\right) t\right]$

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

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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(II) The displacement of a…

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the equation of a transver…

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$\bullet$ The equation des…

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The equation of a wave tra…

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A wave on a string is desc…

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The equation of a transver…

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The transverse displacemen…

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A transverse wave on a str…

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A wave on a string has a w…

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Okay. The given we've is be even which is equal to 4.2 Sign off 0.84 x minus 47 p plus 2.1. We have to find the question off Live, which is moving, opposes side. So the very question D two will be equal to 4.2. Sign off. Do you don't? Point 84 x plus 40 70 plus 2.1. This is the the which is traveling. Oppose it toe even. No. The equation for standing wave Isham off the two component Web so we can write De resulted will be cool toe de even plus D to now we know that sign theater one less sign Theater, too, is a cool toe to off Sign Teton. Let's theater two by two into cause off theater one minus theater toe divided by two. We will use this trick dramatic equation while calculating with militant standing with so dear will be equal toe de even which is four point toe sign off. 0.84 x minus 47 p plus 2.1 Bless four point to sign off. 0.84 x plus 40 70 plus 2.1. Now we will ride this 4.2 in tow dries off. Sign theater one plus theater, too divided by two so you can write 0.84 x plus 2.1 in tow Cause off. This is equal to theater one, and this is equal to theater, too. So cause off hitter and minus theater toe divided by will be equal to minus 47 into T. Now we can write resultant equation off the standing way with equal toe 8.4 sign off zero point 84 eggs less two point when into cause off 40 70 Because we know that cause off minus theater is a call to cost theater So this is our answer for part B.

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