6. Summary
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- 2163
The main concepts from this chapter are:
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A material wave is a propagating disturbance in a material, while the atoms that make up that material do not travel very far.
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Waves describe a large range of phenomena such as ripples in a medium, pressure fluctuations in sound or even fluctuations that describe light.
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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.
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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.
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The wave function and the total phase are function of space and time; knowing only one is not good enough.
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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.
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The wave velocity \(v_{wave}\) is set by the medium.
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The frequency \(f\) is set by the source.
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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 |
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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!