Sound overview (2 min)

Waves - sound wave model (5min)

Waves - light, speed (5min)

Waves - Speed on strings (1 min)

Waves - boundaries (4 min)

Sound wave example (9min)

wave pulse down string masses and pulley example (9min)

Summary

Summary

Atomistic Goals

Students will be able to...

1. 1. Be able to take a physical phenomena and represent it as a history graph or a snapshot graph.
2. 2. Be able to identify distinguishing features of mechanical, E&M, and matter waves.
3. 3. Be able to mathematically model a traveling wave using a function that has the form of $D(x,t)=D_{max} \sin(kx-\omega t)$ and be able to manipulate this equation to find relations between D, v and a.
4. 4. Understand the connection between waves and oscillations.
5. 5. Understand that the frequency of a wave is dependent only upon the source.
6. 6. Understand that the speed of the wave depends on the medium in which it travels.

In this video Doc Schuster gives a thorough introduction to wave motion as a function of x and t. 

https://www.youtube.com/embed/GxAyRJjCAsQ

Here is Doc Schuster giving a good run down of this section on Traveling Waves,

https://www.youtube.com/watch?v=a89X1fXeVkw

Other Resources

This link will take you to the repository of other content related resources .

This link takes you to the PhET simulation for travelling waves.

You don't need Java to run this application.

For additional simulations on this subject, visit the simulations repository.

Sound waves in water

https://www.youtube.com/watch?v=uENITui5_jU

Oh no, we haven't been able to write up a history overview for this topic. If you'd like to contribute, contact the director of BoxSand, KC Walsh (walshke@oregonstate.edu).

Light as a wave

https://www.youtube.com/watch?v=IRBfpBPELmE

This site by Dan Russel at PSU uses a number of animations to explain the modes of waves.

The Physics classroom discusses the difference between standing waves and traveling waves.

Hyperphysics's concise reference for traveling waves.

Hyperphysics actually has several sections related to traveling waves. Using the concept map, click on the sections down the second path from the left.

Waves Introduction	Transverse Waves
Longitudinal Waves	Wavelength and Frequency in Relation to Sound

The University of Louisville Department of Physics has a nice overview page with great animations.

This web page has several animations showing the different types of waves, and covers the mathematical representation in a suscinct matter.

Other Resources

This link will take you to the repository of other content related resources .

Resource Repository

This link will take you to the repository of other content related resources.

Remember that frequency is what determines a wave's energy, and as such cannot change as it travels since energy must be conserved. Instead, the wavelength, $\lambda$ is the thing we always assume changes as a wave travels through different mediums. Also since $v = \lambda f$, velocity will change as $\lambda$ changes.

It is also worth pointing out that period, $T$, and angular frequency, $\omega$ are related to frequency like so:

$T=\frac{1}{f}$ and $\omega = 2 \pi f$

As such, a wave's period and angular frequency are also properties of the wave itself and not the medium and will not change as the wave travels. Also since color is tied specifically to frequency, color will also not change as the wave enters different mediums.

When solving a traveling wave problem you will most likely be using the wave equation $D(x,t) = Asin(kx - \omega t)$. Remember that $k = \frac{2 \pi}{\lambda}$ and that $\omega = 2 \pi f$ where $\lambda$ is the wavelength and $f$ is the frequency of the wave.

Graphical problems:

Draw a physical representation of your system and label any quantities given in the problem statement. It is a good idea to either draw a sketch of $x$ versus $t$ or an overhead snapshot of the situation, depending which is appropriate - for example, for the motion of a particle in a vibrating string, $x$ versus $t$ is more appropriate; for analyzing ripples on a pond radiating from a point, the overhead view will be more appropriate. Label wavelengths and/or periods.

Graphical problems will typically ask you about how many cycles will pass a point in a given amount of time, or how many wavelengths will fit in some area. Remember that a wavelength is a distance in meters that tells you how far a wave must travel to be at the same point in its cycle; the period is a time that tells you how long a wave must propogate for before it returns to the same point in their cycle. 

Other problems:

Identify the type of wave - is it mechanical or electromagnetic? If it is an electromagnetic wave then you immediately know that its traveling with speed $ c = 3 * 10 ^ 8 $ m/s, and you can quickly find the wavelength if given the frequency, and vice-versa. Recall that $v_{wave} = f \lambda$. A common question when considering traveling waves is how long it takes a wave to travel from point A to point B. Understanding the wavespeed makes this problem easy - the distance is just $d = v t$.

 All of the mathematical operations inside of the cosine/sine function can make the wave equation look intimidating, but are simple to handle case-by-case. For example, say you have the following equation - $D(x,t) = A sin( 30x - 50t) $ - and you are asked what are the wavelength and period of the wave. A good way to remember which terms are associated with wavelength and frequency is to inspect the equation and notice that there is an $x$, which we typically measure in meters, and $t$, which we measure for time. Since we want the argument inside of a trig function to be dimensionless, we know that $x$ is associated with wavelength and $t$ with the frequency or period.

Since the wave equation is $D(x,t) = Asin(kx - \omega t)$, we know that in the previous example

$$k = \frac{2 \pi}{\lambda}$$

$$⇒ \lambda = \frac{2 \pi}{30} = 0.21 m $$

and 

$$ \omega = 2 \pi f $$

$$⇒ f = \frac{\omega}{2 \pi} = 8 s^{-1} $$

$$ T = \frac{1}{f} = 0.125 s $$

• Mechanical traveling waves require a medium, but the particles of that medium do not travel with the wave: they propogate the wave by oscillating about some position.
• Electromagnetic waves are self-propogating; they do not require a medium and can travel through vacuum.
• The wave speed $v = \lambda \, f$ is not the speed of the oscillators, it is the speed of the feature of the wave itself.  For example, a traveling wave on a string the oscillators are the tiny pieces of string that move up and down; the wave speed describes the speed of the crest that travels along the string, not the up and down motion.
• Not understanding the SHM nature of each particle in the wave.
• Speed of wave vs. speed of the particles in the wave.
• Use of degrees vs. radians for the function arguments.
• Direction of wave motion not discerned from equation; not connect to sinosoidal graph.
• Water waves are neither transverse or longitudinal waves, they are a combination of the two.
• The linear mass density of a string is the total mass divided by the total length.  Experimentally a commom mistake is to measure the total mass and divide by the length between two fixed ends of the string when the string is clamped and ready to oscillate back and forth to observe traveling waves. 

• $v_{wave} = \lambda * f $ is a really useful equation to have in your back pocket, both for understanding and practicality. Remember that this equation means that the crest of a wave must travel a distance of one wavelength during one period. Practically speaking, this is sometimes a helpful equation to pull out when you have too many unknowns and need another equation.

Multiple Representations is the concept that a physical phenomena can be expressed in different ways.

Physical

Mathematical

Graphical

Descriptive

Experimental