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(II) Show that if damping is ignored, the amplitude $A$ of circular water waves decreases as the square root of the distance $r$ from the source: $A \propto 1 / \sqrt{r} .$

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$A \propto \frac{1}{\sqrt{r}}$

Physics 101 Mechanics

Physics 102 Electricity and Magnetism

Chapter 15

Wave Motion

Periodic Motion

Mechanical Waves

Electromagnetic Waves

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Simon Fraser University

University of Sheffield

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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) Show that if damping …

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A two-dimensional water wa…

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A two-dimensional water w…

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A line source emits a cyli…

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Using energy arguments, sh…

Illustrates that at distan…

Assertion If the length of…

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Verify that the wave equat…

here in this problem we have to prove M flick you'd is proportionally toe one upon on the route are so first you have to assume here the first assumption we have to ask you that all wave motion is along the surface of water. That means no waves are propagating downwards. Suppose this is the surface of water and okay, all the way Emotion is along the surface of water. No wave motion is provocation propagating downward into the water. So we know that intensity. Sorry. Power is equal toe intensity into here. In this case, I suppose this is the radius R to fire. And we know that intensity is proportional to amplitude care square so we can write Power is equal to key A square in tow to buy our kids constant here power is equal to key Is square in tow Fire? No. If there is no damping, that means power is constant. If father is constant, we can right here key a square in tow Two pi r is equal to a constant. That means a square is inversely proportional to one of one R or a is proportional to one upon on the Ruth are

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