a wave is traveling through x. what can be known about x? This is a topic that many people are looking for. amritsang.org is a channel providing useful information about learning, life, digital marketing and online courses …. it will help you have an overview and solid multi-faceted knowledge . Today, amritsang.org would like to introduce to you Traveling Waves: Crash Course Physics #17. Following along are instructions in the video below:
We have an ordinary piece of rope. Its not one of those magicianss ropes that can mysteriously put itself back together once its been cut it half. And its not particularly strong or durable.
But you might say that it does have special powers. Because itll demonstrate for us. The physics of traveling waves.
Ropes and strings are really good for this kind of thing because when you move them back and forth the movement of your hand travels through the rope as a wave by observing what happens to this rope. When we try different things with it well be able to see how waves behave. Including how those waves sometimes disappear completely.
Hows that for a magic trick theme music. This is a typical wave and waves form whenever. Theres a disturbance of some kind often when something about the physical world changes.
The information about that disturbance gradually moves outward away from the source in every direction. And as the information travels it makes a wave shape think about all the disturbance you cause for example when you jump on a trampoline. When you hit the trampoline.
The downward push that you create moves the material next to it down a little bit too and the same goes for the material next to that and so on and while that information is traveling outward the spot. Where your feet first hit the trampoline is already recovering moving upward again because of the tension force in the trampoline. And that moves.
The area next to it upward too this up and down motion gradually ripples outward covering more and more of the trampoline. And the ripples take the shape of a wave waves are made up of peaks with crests the bumps on top and troughs the bumps on the bottom. They have an amplitude.
Which is the distance from the peaks to the middle of the wave. They also have a wavelength which is the distance between crests a full cycle of the wave and a frequency. Which is how many of those cycles pass through a given point every second multiply the wavelength by the frequency.
And you get the waves speed. How fast its going and the waves speed only depends on the medium. Its traveling through thats why the speed of sound.
Which is a wave doesnt depend on the sound itself. It doesnt matter how loud or quiet. It is it just depends on whether the sound is traveling through say air or water now there are four main kinds of waves.
And we can use our rope to show the difference between some of them a pulse wave. Is what happens. When you move the end of the rope back and forth just one time.
One lonely crest travels through the rope. Thats the pulse. Then theres a continuous wave.
Which is what happens when you keep moving the rope back and forth in that case your hand is acting as an oscillator anything that causes an oscillation or vibration can create a continuous wave. Now things that cause simple harmonic. Oscillation move in such a way that they create sinusoidal waves.
Meaning that if you plotted the waves on a graph theyd look a lot like the graph of sin x .
But the waves. Weve mainly been talking about so far are transverse waves ones in which the oscillation is perpendicular to the direction that the wave is traveling in when a wave travels along this rope for. Examplethe peaks are perpendicular to the ropes length.
The same thing was mostly true for the waves that you made on the trampoline. The waves were traveling along its surface horizontally. But the peaks were vertical.
But there are also longitudinal waves. Where the oscillations happen in the same direction as the wave is moving in the case of a longitudinal wave the back and forth motion is more of a compression and expansion. These are the kinds of waves that you get by compressing and stretching a spring and theyre also the kinds by which sound travels which well talk more about next time.
But all waves no matter. What kind they are have something in common they transport energy as they travel at a microscopic level waves. Occur when the movement of one particle.
Affects the particle next to it and to make that next particle start moving there has to be an energy transfer. But how can you tell how much energy. A wave has well remember that an object in simple harmonic motion.
Has a total energy of one half times the spring constant times. The amplitude of the motion squared which means for a wave caused by simple harmonic motion. Every particle in the wave will also have that same total energy of half k a.
Squared all of this together tells us that a waves energy is proportional to its amplitude squared in other words. If you double the waves amplitude you get four times. The energy triple the amplitude you get nine times.
The energy. So why is the relationship between amplitude and energy transport. So important well the intensity of a wave is related to the energy.
It transports more specifically its intensity is equal to its power divided by the area. Its spread over and power is energy over time so changing the amplitude of a wave can change its energy and therefore its intensity by the square of the change in amplitude and this relationship is extremely important for things like figuring out how much damage can be caused by the shockwaves from an earthquake. But waves also get weaker as they spread out because theyre distributed over more area.
A spherical wave for example. One that ripples outward in all directions will be spread over the surface area of a sphere that gets bigger and bigger the farther the wave travels. The surface area of a sphere is equal to 4 times pi.
Times its radius squared . So as a spherical wave moves farther from its source. Its intensity will decrease by the square of the distance from it two meters away from the source and the intensity of the wave will be 4 times less than if you were 1 meter away three meters away.
And itll be 9 times. Less. Thats why being just a little bit farther away from the source of an earthquake can sometimes make a huge difference now lets go back to the waves.
We were making with the rope. Suppose you attach one end of the rope to a ring thats free to move up and down on a rod. Then with your hand.
You send a pulse in the form of a crest rippling along it when the pulse gets to the end of the rope.
The rope slides along the rod. But then it slides back to where it was that motion the sliding back reflects the wave back along the rope again as a crest. But something totally different happens if you attach the end of the rope.
So its fixed and cant move now if you send a pulse along the rope. It will still be reflected. But this time as a trough.
The wave was inverted thats because when the pulse reached the fixed end of the rope. It was trying to slide the end of the rope upward. But it couldnt because the end of the rope was fixed so instead the rope got yanked downward and the momentum from that downward movement carried the rope below the fixed end inverting the wave now sometimes multiple waves can combine for example.
Say you send two identical pulses both crests along a rope. One from each end when the two pulses overlap. Theyll combine to make one crest with a higher amplitude than the original ones.
Thats called constructive interference. The waves build on each other now. Lets say you do the same thing again this time both waves have the same amplitude.
But ones a crest and the other is a trough and when they overlap the rope will be flat. It looks like the waves just disappeared. Thats called destructive interference.
When waves cancel each other out constructive and destructive interference. Happen with all kinds of waves pulse or continuous transverse or longitudinal and sometimes we can use the effects to our advantage noise canceling headphones for example work by analyzing the noise around you and generating a sound wave that destructively interferes with the sound waves from that noise canceling it out theres a lot more to talk about when it comes to the physics of sound. But well save that for next time today.
You learned about traveling waves. And how their frequency wavelength and speed are all connected. We also talked about different types of waves including pulse continuous transverse and longitudinal waves and how they all transport energy finally.
We discussed reflection and interference crash course physics is produced in association with pbs digital studios. You can head over to their channel to check out. Amazing.
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