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(a) Show that if the tension in a stretched string is changed by a small amount $\Delta F_{\mathrm{T}},$ the frequency of the fundamental is changed by an amount $\Delta f=\frac{1}{2}\left(\Delta F_{\mathrm{T}} / F_{\mathrm{T}}\right) f .$ (b) By what percent must the tension in a piano string be increased or decreased to raise the frequency from 436 $\mathrm{Hz}$ to 442 $\mathrm{Hz}$ . (c) Does the formula in part $(a)$ apply to the overtones as well?
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Physics 101 Mechanics
Physics 102 Electricity and Magnetism
Chapter 15
Wave Motion
Periodic Motion
Mechanical Waves
Electromagnetic Waves
Cornell University
University of Washington
Simon Fraser University
University of Sheffield
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. The frequency of a stan…
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A stretched string, of len…
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A musician tunes the C-str…
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While attempting to tune t…
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Two identical taut strings…
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Tuning a cello. A cellist …
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CP Two identical taut stri…
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Tuning an Instrument. A mu…
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A string on a cello has le…
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is this question. We want to know how as a frequency of the fundamental, the fundamental frequency of a string depends on his attention in it. In part, a. We want to see that its attention is changed by Delta ft. We want you know that, don't you? See, that's upon the metal frequency will be changed by the attack if I equals 1/2 if teeth over F or in other words, delta if the percentage change. But as fundamental frequency is half a percentage change off the tension. So let's look at this part we can write down. So definition off some fundamental frequency this because we over Ando and named, uh, just leave it there because it doesn't change, but he s screwed off ft over you so you can see their relationship is in there to have a scholar of two relationships. So in order to find hope, the auto depends on if we will need to take the derivative because iota, huh? Because Steve, the attention, perhaps Dota fish. So we need to find what's this is you have Dina, let's take the derivative. This gives us to Linda over mu ft. And because we wanted in terms of F because we want better if because 1/2 of something f so we want you created this way Hot. We want to substitute the initial small f in chooses. So, um, we can create an f by putting attention Big earth Isa Denominator, Sam, we have cysts, ends that gives us two times 50 of us left. And then we go back to this equation and we get Toto is 1/2 Oh, more over 50 times dear to ft. And we look att, part B, heart pieces. If the cashier of the piano, it's ah, you want to raise a pitch of the piano stream from 436 years 2 442 herds. What should we do to his tension? And so we can do that by rearrange it to have the percentage change of tension on the left hand side, and it is two times a percentage chance off the pitch. So the change of the page is six words divided by his original page is 436 hertz. So it gives us, um, 2.75%. So we need to, um, increased attention by 2.75%. To get to use our desire to pitch Part C does a formula off a apply two's overtones as well. And the master is definitely yes, because we do not. We do not use the relationship off Lambda in terms of Elwood, just say Syria's this Lambda. So it's a very general genetic statements and will apply to Oro virtues.
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