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(II) One end of a horizontal string of linear density $6.6 \times 10^{-4} \mathrm{kg} / \mathrm{m}$ is attached to a small-amplitude mechanical $120-\mathrm{Hz}$ oscillator. The string passes over a pulley, a distance $\ell=1.50 \mathrm{m}$ away, and weights are hung from this end, Fig. $37 .$ What mass $\mathrm{m}$ must be hung from this end of the string to produce $(a)$ one loop, $(b)$ two loops, and $(c)$ five loops of a standing wave? Assume the string at the oscillator is a node, which is nearly true.

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a) 8.7 kgb) 2.2 kgc) 0.35 kg

Physics 101 Mechanics

Physics 102 Electricity and Magnetism

Chapter 15

Wave Motion

Periodic Motion

Mechanical Waves

Electromagnetic Waves

Rutgers, The State University of New Jersey

University of Washington

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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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One end of a horizontal st…

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(II) One end of a horizont…

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In Fig. $16-42,$ a string,…

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A $12-\mathrm{kg}$ object …

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A $12.0$ -kg mass hangs in…

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Two waves traveling in opp…

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A 12.0-kg object hangs in …

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A 12.0 -kg object hangs in…

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One end of a long string o…

is this question. We have a string. So it is staying over a pulley and has a match Attest to it. Silence of the string is one point. Find several meter and the linear intensity is 6.6 time. Tend his negative four kilogram per meter. And we won't You know what is a mask off end so that the string can produce one loop to loops or five groups. So we can do that by looking for the fundamental frequency of, um, off the stream. Because so when it produces two loops, it's just two times a fundamental frequency. And when they're five groups, we have five times a fundamental frequency. So the fundamental frequency if n it equals end times um So any frequency equals n times a fundamental pregnancy, fundamental frequency if one, um, equals feet over them, della. But at the same time, because every coffee over Linda. But at the same time, we know that four of the most fundamental first harmonics lambda equals to l. So we have it was envy over to L now thinks it's a transfers wave on a string. We also have this relationship for these at B equals ft over new an empty equals mg. So this is a four meter we have and we can see that we have everything we need except m um, so we can really French this equation so that we have em. He close for every square fm skirt you over in square G. So for f n. We know that. So all the mechanical oscillator of here has a fixed frequency of 120 years off apart by one only have one loop sack response to an equals one, so n equals four times L square times 120 Hertz square. I'm Samuel is 6.6 times 10 cheesy. Make that four here. Gram per meter and square is one G is 9.80 meters per second squared. So this is 8.7 to 8 kilograms, which is roughly 8.7 kilograms for part B. We do not actually need to go through the whole calculation because we can see the only sense going to change his n. So for he orders you have two lips if it goes from 2 1 to 4. So m two is one force of everyone which is to want to kill them. Same if I equals 25 times in one because we go from, uh, one loop to five groups, that is, you know, 50.35 kilograms.

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