412 Quiz 1

Phase front

• Surfaces of the waves

• Spherical plane waves look like water ripples

• Plane waves are rectangular in shape and propagate in a uniform direction, creating wavefronts that are parallel to each other.

Phase velocity

• The phase of the wave is constant throughout the entire x-y plane

• phase velocity or speed of sound is symbolized by a c

• c is a material property

• c is constant in its medium

Plane wave equation

Dispersion Equation

• related to material property density and compressibility

Dispersion Diagram

• non-dispersive media is a linear relationship between frequency and wave vector, meaning that all frequencies travel at the same speed.

• non-dispersive materials are water and air

• dispersive media and result in a variation of wave speeds depending on frequency, which can lead to phenomena such as wave distortion and the formation of different wavefronts.

Material property density

Material property compressibility

Speed of sound

• is also call phase velocity

• depends on temperature

• constant for every frequency

Relationships between equations

• c = (density * compressibility) ^-1

• Compressibility is inversely related to stiffness

• phase velocity is inversely related to the square root of density\

• Therefore phase velocity is related to the square root of stiffness

Fourier Theory

• Waveforms can be broken down into sin and cos

Wavelength

• Spatial period of the wave

• symbolized by lambda = 2 * pi / k