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(II) Show that the frequency of standing waves on a cord of length $\ell$ and linear density $\mu,$ which is stretched to a tension $F_{T, \text { is given by }}$$$f=\frac{n}{2 \ell} \sqrt{\frac{F_{\mathrm{T}}}{\mu}}$$where $n$ is an integer.

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$f_{n}=n \cdot \frac{v}{2 l}=n \cdot \frac{1}{29} \sqrt{\frac{F}{\mu}}$

Physics 101 Mechanics

Physics 102 Electricity and Magnetism

Chapter 15

Wave Motion

Periodic Motion

Mechanical Waves

Electromagnetic Waves

University of Michigan - Ann Arbor

University of Washington

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.

02:35

A string has a linear mass…

05:13

Assuming that the wave spe…

02:29

(II) $(a)$ Show that the a…

02:42

(II) A cord of length 1.0 …

06:28

Suppose that a string of l…

Show that the sound wave i…

01:17

A wire of length $2 \cdot …

02:16

A transverse wave describe…

01:26

Two strings, of tension $T…

01:58

02:03

A string with a linear mas…

02:11

this problem We have given the land off gold which is equal to L. And we know that the frequency is expressed days we we speed the word way violent for the fundamental case Suppose this is the cold. It is vibrating like this. So this is a call to left by two. We can write Lambda by two is equal to l. So the wavelength in the fundamental case will be equal toe too well. So the fundamental frequency will be equal toe. We've I do well and we know that that we've the spirit is expressed This a little d attention divided by mean f t Is the tension in that court divided by milk? This is the fundamental frequency. No, the next next harmonic we see. I suppose this is the cool off length l This will be equal to like this and this is equal to Lambda. So in the next harmonic, the frequency will be called tohave toe equal. Do we We just same divided by lambda here. Lambda is equal to l. So we will right earlier. So this will be equal to one upon l under road f b y mu no in the next harmonic. If we see suppose this is the cold. So this will be equal toe like this. Bagram. So this will be cool. Do Lambda plus Lambda by two. That means three Lambda by two. So three them the way to will be equal toe l The Lambda will be equal toe to l by three. So there frequency will be equal toe one upon will weigh three. That means three y two l's under road F t by mu. Now, if we see if one have to have three, we can write F three is equal toe tries off from and have two is equal to twice off everyone. That means f and will be equal toe and times off if one which is the vie Well, all we can write and into one upon to well on the road. Efty blame you. This is the frequency the entire morning, Kish

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