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(II) $\mathrm{A} 65$ -cm guitar string is fixed at both ends. In the frequency range between 1.0 and 2.0 $\mathrm{kHz}$ , the string is found to resonate only at frequencies $1.2,1.5,$ and 1.8 $\mathrm{kHz}$ . What is the speed of traveling waves on this string?

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390 m/s

Physics 101 Mechanics

Physics 102 Electricity and Magnetism

Chapter 15

Wave Motion

Periodic Motion

Mechanical Waves

Electromagnetic Waves

Simon Fraser University

University of Winnipeg

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 guitar string is $65.0 \…

0:00

string fixed at both ends …

01:11

If the fundamental frequen…

01:47

The speed of a wave travel…

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A bass guitar string is 89…

02:28

When a $60.0-\mathrm{cm}$ …

02:02

A string on the violin has…

00:49

A guitar string oscillates…

02:14

(a) Find the speed of wave…

The fundamental frequency …

02:37

A $75.6-\mathrm{cm}$ strin…

A string that is stretched…

02:40

The equation for the speed…

01:39

A 2-m long string is stret…

01:15

A guitar string $66 \mathr…

So a 65 centimeter get her string 6.5 65 centimeter. It's fixed at both ends and in the frequency ranch, which one? And to kill herds, we find the president to be one point you 1.4 in 1.8 and we want to know what's the speed of traveling with. So just by looking at this because we have, um, we see that oh up sees frequencies differ by 300 hertz. So if this is f n says his f n plus one, this is f impressed you. We can see that because, um because the resident frequencies differ last 300 hertz to each other, we can tell that's a fundamental frequency if one equals 300 hertz. So knowing that, uh, we can find we lost a B B equal slammed times F. And of course, the reason we want to find the fundamental frequency is because we want to find the witless that is associate ID weasel frequency. So we can we can It doesn't really we don't really have to use So what we can use f to ease our case. We will have sis weapons in at three, we could have this witness, but usually we go to the fundamental frequency because we find it a lot easier to use this. It's the waves as equals to l um So it's two l f, which is two times serial point 65 meter times, um, 300 hertz. This is 390 meter per second and against this is using the properties of the fundamental wave. If you do not like to see the property upset, another way to do that is you can use policies. For example, after we see, that's a fundamental frequency is 300 hearts who controls at one point you kilohertz is fourth harmonics 1.5 is 1/5 Hamonic. A month in six is on 60.8 Izzy six harmonics. So, for example, for the 1st 4 Monix, we will have perform like this. In this case, Lambda equals half of L and F equals Well, point you kilohertz. So in this case, we can also see he was half of l. A times 120 hurts. But of course, you can see that it will be the same answer. It would be 390 meter per second

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