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Ch 19: Waves & SoundWorksheetSee all chapters

# Intro to Waves

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Sections
Intro to Waves
Wave Functions & Equations of Waves
Velocity of Transverse Waves (Strings)
Wave Interference
Standing Waves
Sound Waves
Standing Sound Waves
Sound Intensity
The Doppler Effect
Beats

Concept #1: What Is A Wave?

Transcript

Hey guys, in this video we're going to start our discussion on waves with just an introduction what exactly is a wave alright let's get to it. Now what a wave is is it's a moving disturbance and I have chosen a key word oscillation it's not just any kind of disturbance it's a disturbance that goes up and down some kind of oscillation some kind of repetitive movement and it carries energy it's very important to understand that all waves carry some amount of energy and the type of energy that it carries and how to find that energy how to calculate it depends upon the type of wave but all waves from water waves, waves on a string, light, sound they all carry some amount of energy one of the most common examples of a wave is just a wave on a string you can imagine the string fixed to some sort of anchor point like a wall you grab one end of the string right you're holding it with your hand and you're whipping your hand up and down. As you whip your hand up and down you produce a little pulse that travels down the length of the rope at some speed. This is a wave this is only a single pulse of a wave but if you were to whip it multiple times you would produce a continuous wave along that string and the moving strings since the string has mass carries some amount of kinetic energy now we're going to focus ourselves entirely on a type of wave called periodic waves these are waves with repeating cycles and a cycle is defined as a portion of the wave a portion of the motion that begins and ends in the same state. So if you have a wave right and a wave is measured by how much displacement it has from sum 0 let's say that this wave starts with no displacement and it's increasing its displacement it's going in the positive direction then when this wave completes itself it's going to return back to a point worth no displacement where when the wave goes on it's going to be moving up. So the same state of motion same position same direction of motion. You could also consider a wave that is already starting with some displacement and then it's going to go down and up and down again until it reaches that same height and both of these are going down, both of these are examples of cycles a point that begins a portion that begins and ends at the same state. The easiest way to measure a cycle is to just go from peak to peak. That's the simplest way to measure a cycle.

Waves have several important characteristics I've highlighted a few of them you have the period of a wave which is the amount of time a cycle takes how long does it take for a wave to complete one cycle and this is sort of the characteristic time measurement of a wave the frequency which is the number of cycles per unit time so how frequently do cycles appear if you have one cycle per second versus two cycles per second those cycles appear twice as quickly out of frequency of two cycles per second then one cycle per second the wave is appearing more quickly per unit time the wavelength is the distance the wave travels in a cycle, so how far does it travel in a cycle now the period and the frequency are two things that you've seen before in oscillatory motion. Remember we're talking about oscillations for waves so we talked about simple harmonic motion like for a spring a mass on the spring or a simple pendulum you also talked about things like frequency and period but there is an additional aspect of waves that plain harmonic motion doesn't have it has motion it has movement right it is a moving disturbance. So because it's moving across the some distance and the wavelength is how far it travels in a cycle so the wavelength is the characteristic distance of a wave and lastly because the wave is moving it has some sort of speed and I don't need to go ahead and define what speed is for you guys you've seen speed over and over and over again.

Here are a couple of graphs that show some of the wave characteristics we have a graph of displacement given by Y versus time and a graph of displacement given by Y versus horizontal distance vs propagation distance that's the direction of the wave that's travelling in space if I identify a cycle as a peak to a peak so I'm going to go from peak to peak then the distance between two peaks on a time graph is going to be how long a cycle takes which is by definition a period and period we give with the symbol capital T if I identify a peak to peak on our displacement verses position graph peak to peak this is one cycle on the displacement verses position graph so this is how far it travels in one cycle which we call the wave length which we get by the Greek letter and im both these instances we can mark the amplitude which is just the maximum displacement of that wave. Now there's a fundamental relationship between the wavelength and the period or the wave length and the frequency of a wave we can say that the speed of a wave is by definition how far it travels divided by how long that takes right so how far does it travel in one cycle the wavelength how long does that take the period right this is for a single cycle for two cycles it will be two wavelengths and two periods for three cycles it will be three wavelengths and three periods but either way it's going to simplify two wavelength divided by period. We can rearrange this equation and say this is also equal to the wavelength times the frequency because we know the relationship between the frequency and the period is F equals 1 over T. This equation right here that the speed equals lambda F is one of the fundamental wave equations that you guys absolutely need to know. So let's do a quick example, a wave has a speed of 12 meters per second and a wavelength of five meters, what's the frequency of the wave? And what's the period? Well what equation do we know that relates speed, wavelength, frequency, period. We have V equals lambda F and if we want to find the frequency all we have to do is divide lambda over right we know the speed we know the wavelength, we want to find the frequency.

So the frequency is V over lambda which is 12 meters per second divided by 5 meters you want to make sure that the distance unit here is the same when in doubt just use SI units but if the speed was centimetres per second and the wavelength was centimetres you could still do this division because those centimetres are going to cancel but if one was centimetres per second and the other was meters or millimetres or any other unit you could not do this division. Just make sure there are consistent units and 12 divided by 5 is about 2.4 hertz. That's the frequency now we want to know the period a quick way is to use a relationship right given right here of the frequency to the period so the frequency is 1 over the period which means if I multiply the period up and divide the frequency over I can say just as equivalently that the period is 1 over the frequency this is 1 over 2.4 hertz which is 0.42 seconds. Alright guys that wraps up our introduction into what exactly waves are thanks for watching.

Example #1: Properties of Waves from Graphs

Transcript

Hey guys, let's do a quick example about waves. What are the properties of the following wave? Wave length period frequency and speed given in the graphs, so we have two graphs we have a position sorry a displacement vs position and the displacement vs time graph. Displacement vs position is going to tell us things about distances and displacement vs time is going to tell us things time now going from peak to peak we can define one cycle the distance that one cycle takes is the wave length but we're only given half that distance right from the peak to a trough is one half of the wavelength so we can say one half of the wavelength is 2 centimeters which means that the wavelength is just 4 centimeters right double that easy. Now the peak to the peak on a time graph will give us the period and that time as were shown is 5 seconds so we know that the period is 5 seconds. So we know the wavelength and the period now we need to find the frequency the frequency we can find from the period really easy we can just say that the frequency is one over the period which is 1 over 5 seconds which is 0.2 hertz, very easy

Let me give myself just a little bit of space we know the frequency now and finally, we want to know the speed the speed equation. can either be the wavelength over the period or it can be the wavelength times the frequency it doesn't matter which one you use since you know all three of these pieces of information but I'll just use 4 centimeters times 0.2 seconds which is 0.8 centimeters. per second and that's the speed. Alright thanks for watching guys.

Example #2: Distance Between Crests

Transcript

Hey guys, I hope you're able to solve this problem on your own if not here's a little bit of help a wave moves with a speed of 120 meters per second if the frequency of the wave is 300 hertz what is the distance between the wave crests? Distance between wave crests so if you have a wave that's going up and down and up and down and up and down what do we call the distance between the crests? Well each crest is a new cycle and the distance between those crests is just going to be the wavelength so what we're asking what the question is asking for is the wavelength right the distance travelled during one cycle. So if we know the wave speed and we know the frequency how do we take that and find the wavelength using our standard wave equation we'll just say that the frequent sorry the speed is a wave length time the frequency.

We can then divide the frequency over too big. We can then divide the frequency over and say that the wavelength is the speed divided by the frequency which is 120 meters per second divided by 300 hertz which is 0.4 meters that is the wavelength and therefore the distance between wave crests. Alright guys thanks for watching.

Concept #2: Types of Waves

Transcript

Hey guys, in this video we're going to talk about types of waves alright it turns out that you can divide waves into two broad categories called transverse waves and longitudinal waves so we want to know what makes a wave transverse and what makes a wave longitudinal so let's get to it. Remember that a wave is a moving oscillation it's a moving disturbance and that disturbance is oscillatory that means that a wave has to have two directions that are important an oscillation direction. What way do those oscillations go do they go up and down do they go forward and backwards do they go side to side and it has to have motion direction motion we will often refer to as propagation so I will use those words interchangeably. Now as I said the two broad categories of waves that we can dump everything into are transverse waves and longitudinal waves and the difference between the two is the relationship between the oscillation direction in the propagation direction and transverse waves oscillation is perpendicular to motion or to oscillation for longitudinal waves the oscillation is parallel to the motion or to the propagation. Transverse waves are very very easy to draw imagine having a string anchored at a wall and you can hold on to the free end of the string and you just whip it up and down you're producing these pulses that are all travelling along the length of the string so they're travelling horizontally and the vertical position of the string is going up and down up and down so there's an oscillation in the vertical position of the string that's along the Y axis its vertical so it's propagating along the X axis horizontally and oscillating along the Y axis vertically so this is clearly a transverse wave the oscillation direction is perpendicular to the propagation direction now let's take a very common example of a longitudinal wave we have a spring anchored to a wall where you can grab the free end of the spring but instead of whipping it up and down you push it back and forth what that's going to cause is this going to cause travelling clumps of compression along the spring so you're going to get areas where the spring is stacked up really really really close to one another this area of compression and then you have areas of the spring where it spaced very very far apart it's stretched and this is technically called rarefaction and you get oscillating compression in rarefaction compression rarefaction along the propagation direction of ok so this oscillates back and forth along the same direction that the waves are moving this is why this is a longitudinal wave. Now both types of waves have to carry energy because all waves carry energy sorry transverse waves can carry energy of multiple types they can carry a whole bunch of different types of energy and it really depends on the type of wave that it is.

A wave on a string which as I showed above is a transverse wave carries mainly kinetic energy due to the motion of the string but it also carries some potential energy because the string actually stretches when you whip it you have to increase the length to allow for these hills and valleys so some compressed so some potential energy due to the stretching of that string. Water waves carry a ton of kinetic energy a tsunami can be 100 feet tall all that water has a lot of mass and it's moving very very quickly maybe 100 kilometres an hour so that carries a ton of kinetic energy light on its own carries something called electromagnetic energy but light is not something we're going to cover here it's something you're going to cover much later on in physics now longitudinal waves mainly carry energy in the form of potential energy due to compression. The most common type of longitudinal wave is a compression wave in some sort of elastic medium so if you look at the spring springs are clearly elastic, they can stretch they return to the original configuration they can compress they return to their original configuration so the energy is carried by the potential energy due to these compressions which are collapsing it into a smaller sorry distance than it should be and rarefactions which are stretching it to a larger length than it should be both of those give it potential energy so there's a lot of potential energy in this wave sound carries energy on its own too but sound is actually just a type of compression wave in an elastic medium gases liquids and solids which are all media that sound can propagate in all have elastic properties and as we'll see later on sound is just a compression in these elastic media.

Alright guys so we have remember guys we're focusing on a periodic waves right waves that have repeating cycles and periodic waves regardless whether they're transverse or longitudinal obey the same equations they have the same characteristics that you can describe you can talk about amplitudes wavelength period speed frequency all the same characteristics and they obey the same speed relationship lambda F its very important to remember that regardless of whether it's a longitudinal wave or a transverse wave they obey the same relationship. Lets do a quick example can longitudinal waves propagate in a fluid what about transverse waves absolutely longitudinal waves can propagate in a fluid because as your compressing the fluid the fluid wants to not be compressed it wants to return to its original size, fluids are very very resistant to compression so they can propagate compression waves very easily like sound alright now the problem is can they be transverse waves no transverse waves do not propagate very very well in liquids at all the reason is is that if you think about the actual molecules inside of the wave sorry inside of the fluid when you give it some sort of lift right you want those molecules to start going up and start going down right like a wave while it propagates in this direction but the problem is that centrally to the wave is oscillation so as this water molecule goes up it has to come back down but there's no elasticities there's nothing to bring it back this is different than a wave on a string when you whip a wave on a string the wave stretches to allow part of it to go up and that stretching stores potential energy that snaps it back down but there's nothing holding those water weight those water molecules in place so longitudinal waves propagate very very well in fluids right I chose to talk about a liquid here but its the same for a gas and they propagate very poorly in transverse waves. Alright guys that wraps up our discussion on the types of waves. Thanks for watching.

Practice: A satellite captures images of a tsunami, and properties of the tsunami can be found from these images, providing important information to people who need to evacuate coastal areas. If satellite images of a tsunami show the distance from one peak to another is 500 km, and the period is 1 hour, how much time do people have to evacuate if the tsunami is found to be 100 km off shore?