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(II) Determine if the function $D=A \sin k x \cos \omega t$ is a solution of the wave equation.

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$\frac{\partial^{2} D}{\partial x^{2}}=\frac{1}{v^{2}} \cdot \frac{\partial^{2} D}{\partial t^{2}}$

Physics 101 Mechanics

Physics 102 Electricity and Magnetism

Chapter 15

Wave Motion

Periodic Motion

Mechanical Waves

Electromagnetic Waves

Cornell University

University of Washington

Hope College

University of Sheffield

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.

02:34

Given the wave functions

02:06

A standing wave's fun…

01:24

Show that$$\psi(x, t)=…

08:39

Let $\quad y_{1}(x, t)=A \…

04:31

Show that the functions ar…

03:07

in this problem, we have to deter mined. If the function d is equal toe, a sign kicks into cause when we got the we have two little mind. It is a solution off the way, the question or not. So we know that if any wave equation which satisfy del square be divided by their Lexus Square is equal toe run upon we Squire into del squaring toe be del P square. If any question which satisfy this equation, then we can consider that this equation is a solution off wave equation. Yes. Now we'll find the L. D. By Daleks. This will be equal to okay, cause cakes into cause regular t and again partial differentiation with respect to X. So this will be equal to again differentiation off this function with respect to X. So this will be equal to minus K square a signed K X in tow cause Omega T Now we will find there'll be differentiation off Be with respect to time. So we get this will be equal to minus omega a into sign cakes into sine omega t Now again, differentiate it with respect to time we get. This will be called to minus Omega Square A and to sign K X in tow. Course Omega T. If we see this vote equation, we can get these equations satisfied. Okay. Squared, divided by omega is quiet into, then square being tune. Lt square. We know that V is equal toe omega viikii so we can write here. We can write one upon we square into Dallas Square D divided by lt Square So now we can see dysfunction in solution off the equation.

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