Introduction
Waves are everywhere around us. Light waves, sound waves, brain waves, water waves - they're everywhere! Waves are traveling through the electricity in the walls. Waves are eminating from the cell phone in your pocket. Waves are bouncing off of your skin, entering your ears, and rumbling under your feet.

Waves are really rather mysterious. You can't grab a wave, but you can feel it. You can't capture a wave, but you can record it. Even the very definition of a wave is mysterious - "A wave is a traveling disturbance."

In this lesson, we will learn how waves can be described with the language of physics. In the process, we will encounter some of the foundational ideas that are essential to making beautiful music. 

Lesson

• So, what is a "traveling disturbance"? Consider the wave in a sports stadium (like in this YouTube video: http://youtu.be/H0K2dvB-7WY). The wave travels all the way around the stadium, but it is composed only of people standing up and down. In a very real sense, the way is traveling - we can see it as it moves - but none of the people are actually running all the way around the stadium. What is traveling is a disturbance (people standing up and sitting down). The people, in this case, represent the medium of the wave. The medium is the thing that is being disturbed, the thing that the way is traveling through. Every wave has some medium that it disturbs. What do you think is the medium for the following types of waves:
• Water waves
• Sound waves
• Waves on a plucked guitar string
• Waves from an earthquake
• There are two main types of waves that we will be concerned with throughout this unit - transverse waves and longitudinal waves. Examine the first portion of this web page (http://www.acs.psu.edu/drussell/Demos/waves/wavemotion.html) for a brief description and animation of each wave type.
  
  
• Notice how the red dot in both animations illustrates that the individual dots are simply moving up or down (transverse) or left-to-right (longitudinal) in a fixed region, but the disturbance of the wave continues to travel the whole length of the animation. 
  
  
• It is worth noting that sound waves are longitudinal waves, with individual molecules of air moving back and forth along the direction of the sound waves' motion. The disturbance caused by a music speaker or our vocal chords causes areas of higher air pressure (where lots of air molecules are close together) and areas of low air pressure (where air molecules are more spread out.)
  
  
• Let's practice making some waves of our own. Visit the Wave on a String simulation (http://phet.colorado.edu/en/simulation/wave-on-a-string) and click the "Run Now" button.
• Wiggle the wrench to make a wave. What type of wave are you making?
• At the bottom of the screen, check the buttons "Oscillate" and "No End"
• Explore what the amplitude and frequency sliders do - come up with a definition for amplitude and frequency based on what you find.
• How does changing the damping affect the wave? What must "damping" mean?
• Switch to pulse mode and turn the damping completely off. Send a pulse wave down the string and out the window.
• Experiment with the tension slider to determine what the tension (or tightness) of the string changes about the pulse wave. 
  
  
• Now, let's make some sound waves. Visit the Sound simulation (http://phet.colorado.edu/en/simulation/sound) and click the "Run Now" button. (Say "Yes" or "Approve" or "Keep" if you are asked about downloading or installing a small piece of software.)
• Stay on the first tab of the simulation called "Listen to a Single Source."
• The speaker is creating a longitudinal sound wave. Using the sliders on the right, you can adjust the frequency and amplitude. 
• Check the button "audio enabled" to hear the sound from your computer.
• Change the frequency slider. What practical impact does this have on the sound?
• Change the amplitude slider. What practical impact does this have on the sound?
• See if you can play a simple song by using the frequency slider. (It's harder than it seems.)
• In conclusion we can say that the frequency directly impacts the pitch of the sound. The higher the frequency - the higher the pitch. 
  
  
  

Assignment
You may have notice in the Sound simulation that the frequency was given as a number in "Hz" or "Hertz". The number of Hertz is a measure of the number of wave peaks passing a fixed location each second. So, when the Sound simulation began set to 500 Hz, that meant that 500 wave peaks were passing our ears each second.

The Wave on a String simulation does not specify how many Hertz the frequency is set to - it just uses a number between 0 and 100. Let's try to figure out how many Hertz this number represents.

• Visit the Wave on a String simulation (http://phet.colorado.edu/sims/wave-on-a-string/wave-on-a-string_en.html)
• Set the buttons to "Oscillate" and "No End".
• Check the "Timer" button in the top of the screen to open a stop watch.
• The frequency is set to "50" by default. Try to determine the actual frequency of this wave in Hetz. (Hint: There are lots of methods you could use - one possible method is to measure the number of wave peaks leaving the door in one second.)
• Check your answer by setting the frequency to "25" and to "75"  and measuring the frequency again. Are you results consistant.
• Return to the main course page and submit your answers for the frequency of the 25, 50, and 75 settings under "MM-1 Investigation". 

Return to Sample Curriculum
Continue on to Lesson 2