Acoustics 4

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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

- 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