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A uniform cord of length $\ell$ and mass $m$ is hung vertically from a support. $(a)$ Show that the speed of transverse waves in this cord is $\sqrt{g h}$ , where $h$ is the height above the lowerend. (b) How long does it take for a pulse to travel upward from one end to the other?
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Physics 101 Mechanics
Physics 102 Electricity and Magnetism
Chapter 15
Wave Motion
Periodic Motion
Mechanical Waves
Electromagnetic Waves
Cornell University
Rutgers, The State University of New Jersey
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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(a) A uniform rope of mass…
is this question. We have a uniform court of less l and mess n so it is hanging verticality and we want to show that the speed of chess. Where's wave off this cord? A squared off she h What is H h? Is a variable. So for any certain point, H is a distance from the bottom. So when we get this expression, we should immediately realize such the speed of traveling. The speed of the wave will not be the same. It's a part. It's the top and its bottom because it's a bottom H equals zero and it's a top H equals l. So how do we find the speed we had this equations of the equals of attention Dubai by you. It's attention, for example, that so let's respect Mew Mew is a mess. Density of it, which is an off l. What is tension at any point? Uh, at any point of the court, attention of it is cost by the gravity off. It's a segment off string that is below it, because it's this about of strangers pulling on this point, and the mask off this monastery is and over L. A Times H because mass density is him over out and we have age, amount of stream. So this is a mass off all the segment of strains that is below a certain point, and we time it by G to get the gravity of his attention of the court. Then we simply find this equation to get square root of H g part B. We want to know how long it takes for opposed to travel from one end to the other. And this is where we need to use calculus because we can see that is the wave travels, its speed changes. So speed is zero at the very bottom. The speed is screwed off. G L A. It's a very talk. So let's write those differential equation. The age, the change of distance equals velocity, tens, time and velocity is square root of h g DT. So we can rearrange it to have DT equals the H over a squared energy. And we take the interval off both sides to get t equals, um, to times t equals you two times itch over G and technically plus a constant. But we start from T bo zero with X equals zero So the constant is just Cyril. And this is integral from zero to l. So that is two times hell over G. That is the time it would take trouble from what? And he's the other.
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