6. Summary

The main concepts from this chapter are:

1. A material wave is a propagating disturbance in a material, while the atoms that make up that material do not travel very far.

2. Waves describe a large range of phenomena such as ripples in a medium, pressure fluctuations in sound or even fluctuations that describe light.

3. A wave function \(y(x,t)\) describes the behavior of the wave. It can be applied to find the displacement of a medium, or the change in pressure for sound, etc.

4. Harmonic waves have the form \[\Delta y = y(x,t) - y_0 = A \sin \Phi (x,t)\] where \(y_0\) is the equilibrium value of \(y(x,t)\) and \(\Phi (x,t)\) is the total phase.

5. The wave function and the total phase are function of space and time; knowing only one is not good enough.

6. Two common representations of waves: \(y(x,t = \text{const})\) vs. \(x\) or \(y(x = \text{const}, t)\) vs. \(t\). What the graphs of these correspond to physically.

7. The wave velocity \(v_{wave}\) is set by the medium.

8. The frequency \(f\) is set by the source.

9. The wavelength depends on both the frequency and the velocity: \(\lambda = v_{wave}/f\).

Below is a detailed summary of the properties of waves and the types of waves they apply to

Property	Found in	Description
Amplitude \(A\)	All waves	The amount that the wave medium displaces from equilibrium. For some waves,like 1-D waves or plane waves, amplitude is constant. For other waves, like sound waves or ripples on a pond, amplitude decreases with distance from the source
Speed \(v_{wave}\)	All waves	The speed at which the wave moves through the medium (describes motion of the disturbance, not motion of individual particles).
Dimensionality	All waves	1-D: The wave propagates along a line (as on a rope). 2-D: The wave propagates over a surface (as ripples on a pond). 3-D: The wave propagates through a volume (as sound waves or light).
Direction	All waves	Direction the wave travels. For waves that travel in only one dimension (like waves on a rope or plane waves) this takes one of two value: + or -. In 2-D and 3-D waves, propagation may occur outward in all directions
Polarization	Most waves	Direction of medium displacement with respect to the wave: longitudinal waves displace in the same direction as wave; transverse waves displace perpendicularly to the direction of wave motion.
Period \(T\)	Repetitive waves	The amount of time in between successive crests or troughs on a wave. Also, the amount of time in between identical configurations of a periodic wave
Frequency \(f\)	Repetitive waves	The number of crests or identical pieces that occur in a wave during a time of one second. \(f= \frac{1}{T}\)
Wavelength \(\lambda\)	Repetitive waves	Distance between consecutive crests or identical pieces of a wave.
Fixed phase \(\phi\)	Harmonic waves	Sets conditions for the wave at \(t=0\) and \(x=0\)
Total phase \(\Phi\)	Harmonic waves	Incorporates information from \(\phi\), \(T\), and \(\lambda\) into a new quantity to conveniently answer questions about a wave for any \(x\) or \(t\). Waves repeat when you increase or decrease \(\Phi\) by increments of \(2\pi\).

Almost all of physics 7C builds on these main ideas. Make sure you have a solid grasp of them!