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Circular, Spherical, and Plane Waves

ex. ripples in a pond

• 2D ~ circular
• 3D ~ spherical
• far away, spherical waves behave like plane waves

Fundamental Wave Properties

1. Huygens’s Principle

consider a sound wave passing through air

• each air molecule emits a spherical wave
• total wave = sum of all these spherical waves

Each point on a wave front acts as the source of a spherical                                                 wave

• Spherical waves are strongest in direction of the wave motion
• (force of wave + or - spherical wave)
• Note that the wave will spread out at the edges, therefore the wave will get larger as it goes.

2. Superposition (wave addition)

• 2 waves can occupy the same point in space without altering each other
• The resultant wave has an amplitude equal to the sum of the two amplitudes

• Sound waves can cross each other and still remain unchanged
• ex. Talking in a crowded room and still hearing the singular conversation

3. Inverse Square Law

• In 3-D, wave intensity decreases as
• Ex. A teacher stands 4 m from the first row of students in his class. The intensity at which the students hear his voice is 1/42 = .0625

Why?

• Energy is constant, but the surface area grows. Therefore the energy is diluted across the surface area
• surface area of a sphere = 4πr2
• Intensity ~ 1/ Area ~ 1/r2
• In 2-D: Wave spreads out over a circle
• therefore the Intensity ~ 1/ Circumference = 2πr2
• In 1-D: Intensity doesn’t fall off at all

4. Polarization

• A property only of transverse waves (therefore, not a property of sound)
• polarization = direction of oscillation (vertical or horizantal)
• reflected light is polarized parallel to surface it reflects off of
• application: polarized sun-glasses which let in only one direction of oscillations, and therefore decrease the amount of light reaching the eyes