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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!