Waves - Waves Notes
Two important facts about waves:
1) A wave is a traveling disturbance
2) A wave carries energy from place to place <-- This is the primary function of a wave!
When an objection undergoes a repetitive motion (AKA oscillating), it also disturbs the medium surrounding it.
Notice above the water droplet is falling down into relatively still water and as soon as it hits, it disturbs the water around it, sending a wave in 360 degrees outwards from the source of the disturbance.
This means that the medium is the matter that the wave propogates (synonym: travels) through. In the above image, the rippling water is the medium.
QUESTION: What are some other examples of disturbances and mediums? Write two examples of a disturbance/medium pair. Prepare to share these aloud.
Below, you can see multiple rings of waves leaving the central disturbance point. We call these wave fronts and there is an arrow pointing to just one of them in the picture below.
From the side, you can identify wave fronts visually like this:
Credit to H.L.Tam for the image
So far we've been describing mechanical waves, waves that require a medium to travel. Next year in AP Physics 2, we talk about electromagnetic waves (such as light), which do not require a medium (can travel through a vacuum).
To repeat for emphasis: mechanical waves require some sort of medium to pass through (e.g., a solid, liquid, or gas). It is the particle interactions that make the propagation of the wave possible.
There are two types of mechanical waves: transverse waves and longitudinal waves.
A transverse wave is also known as a 'shear wave'. The disturbance travels in a perpendicular direction compared to the direction of the wave.
A longitudinal wave is also known as a 'compression wave'. The disturbance travels in a parallel direction compared to the direction of the wave. Longitudinal waves contain sections of compressions and rarefactions.
ACTIVITY: This would be a great time to grab a slinky from the front and make each type of wave! Get up, go!
The anatomy of a transverse wave consists of the following items: equilibrium, amplitude, wavelength, crest, and trough. Although they're not physical features, they are still described visually: frequency and period.
Equilibrium is the resting position, as if the wave was just a flat line with no y-value height, like the x-axis.
Amplitude is distance from equilibrium to the highest point or the distance from equilibirum to the lowest point. Amplitude is measured in meters because it is a distance.
The crest is the highest point on one wavelength.
The trough is the lowest point on one wavelength.
A wavelength is a measurement of length (meters) from two identical spots on a wave, such as crest-to-crest or trough-to-trough. Each wavelength only has one crest and one trough.
The period of a wave is the number of seconds it takes for one complete wavelength to go by a fixed position. In student lingo, it is "the time for just one wave."
The frequency is the number of wavelengths you have pass by a fixed position in one second. Another way of saying it would be, how many waves 'happen' in one second. Frequency is measured in hertz, which is shortened to Hz.
QUESTION: For each image below 00000000000, what do you measure for the wavelength, frequency, period, and amplitude?
Surface waves have characteristics of both transverse and longitudinal waves.
QUESTION: Why do you think the top layer are complete circles while the bottom layer transitions to flat lines?
LINK: This is an awesome explanation of Wind Waves. (You'll have to view this on a desktop, since it is Flash it will not work on an iPad or iPhone, sorry). I have embedded an animation of it below:
All of this has led us to our first equation for waves, for wave speed. It is simply the wavelength times the frequency. The wavelength is measured in meters and the frequency is in Hz. The wave speed is measured in meters per second, m/s. The symbol for wavespeed is a v, the symbol for wavelength is the greek letter 'lambda', and the symbol for frequency is the script letter 'f'.
If you remember from a previous unit, frequency is also equal to the inverse of the period. The bottom equation is merely showing you the substitution of these terms for another way to solve wavespeed.
QUESTION: Solve for wave speed in the following problems: 0000000000000
Wave speed is dependent upon the medium that the wave is in. The medium's density affects the ability for the wave disturbance to propagate. This can be shown easily via two cups and a string. If you talk in one cup, you might not hear anything in the other unless the string is pulled tight. Can you figure out where the tension in the string belongs in the following equation?
QUESTION: 000000000000
Reflection is the change in direction of a wave when it encounters a boundary and bounces off, staying in the original medium. When waves reflect, the angle of incidence equals the angle of reflection.
When a wave encounters any boundary between different media, some of the wave is reflected back. Some can be absorbed into the new medium.
There is a great website that explains this with an animation. To quote this website:
| We say that a wave reflects when it is turned back at the edge of a medium. The edge of the medium may be fixed, that is, the edge may not be free to move. Or the edge of the medium may be free to move, in which case it is often called an open end. We will imagine a wave pulse traveling down a linear medium such as an elastic rope. |
The following two animations demonstrate how the phase of the wave pulse is affected upon the reflection of the wave.
Wave Reflection, Fixed End Animation
Wave Reflection, Open End Animation
To summarize reflections at a fixed boundary:
If the end is fixed, the reflected wave will be opposite in shape (AKA Phase). If the end is allowed to move, the reflected wave will be the same shape (AKA phase).
If the reflection occurs at a change in medium, some energy is transmitted into the new medium (called a partial transmission). The wave transmitted into the new medium will remain the same phase as the first wave (the incident wave). Some energy is reflected back (as a reflected wave).
High wave speed medium to low wave speed medium: reflected wave is opposite in phase
Low wave speed medium to high wave speed medium: reflected wave is same phase
QUESTION: 000000000000
Superposition and Interference
The principle of superposition says when two waves meet they each pass through each other unharmed (like two ghosts!). At the one moment in time when they occupy the same space, the result is the sum of the amplitudes of each wave at that spot.
Whenever two waves occupy the same region in space they are said to be interfering. This interference either results in a buildup to a higher crest or a deeper trough, or it results in a muted, lesser crest or trough. The official terms are constructive and destructive interference.
Go here to witness interfere
Standing Waves and Resonance
The frequencies where standing waves are produced are called natural or resonant frequencies. However, you don't get a standing wave for all frequencies.
You can see this in motion (albeit very slow motion) here:
This actually occurs much faster in real life, so faster that it looks like the bubbles are 'standing still'.
ACTIVITY: We have lab equipment called "The Wiggler" that demonstrates this principle. Stop what you're doing and assemble the lab equipment so you can get a real life demonstration of this phenomenon.
Go here to witness interference.
Can you figure out how this video is related to standing waves?
This video actually explains some of the science a few minutes in.
The first, lowest frequency that produces one antinode is called the fundamental frequency. The following diagram describes each frequency. As the number of antinodes increases, so increases the harmonic number.
Now that you know what standing waves look like, we can do some math to describe these waves. The following equation describes the wavelength of a standing wave along a string:
L is the total length of the string and n is the harmonic number.
QUESTION: 000000000000
Lastly, we need to define the terms refraction and diffraction. Before I show you ../../images of each, keep the following facts in mind. Both of these terms involve "bending", but refraction happens at the boundary between two different mediums and diffraction occurs all within one medium.
When a wave passes into another medium at an angle, and the new medium has a different wave speed, the wave will change direction at the boundary. This change in direction is called refraction.
The bending of a wave as it passes through a small hole, around a small obstruction, or around the edge of a large obstruction is called diffraction.
