Here is a problem to help you generalize and abstract some of the concepts you have learned.

        Imagine that you have a vacuum cleaner with a hose.  You do not have any attachments connected to the end of the hose so what you have is  the hose with nothing attached when you turn on the vacuum cleaner.  Answer the following questions.  As you answer these questions remember that the pitch (That's "pitch" in a musical sense!) of the sound that you hear is really a measure of the speed of the motor in the vacuum cleaner.  The higher the pitch is, the faster the motor is turning.

• When you turn the vacuum cleaner on the motor will run a some particular constant speed.  When you place your palm over the end of the hose, will the pitch rise or will it fall?
• Explain why the pitch rises or falls when you put your palm over the end of the hose.  If you want, you can use an electrical analogy for your explanation, but you must explain the purpose of all the parts of the circuit if you use an electrical analogy.
• In your electrical analogy, explain the behavior of the system at the limits (like when you don't have your palm on the end of the hose.)
• If you need to make any assumptions about relationships between various variables, identify and explain those assumptions.