Physics 312 Lecture: "Wave Motion II."
Apr 3, 1998
- Sinusoidal waves have equations like
y(x, t) = A sin(k*x - omega*t)
- The speed of a wave may be expressed as
v = wavelength/period = wavelength*frequency
- If one holds time fixed, a sinosoidal wave has
a repeating, sinusoidal shape as a function of position
- If one looks at a fixed position, a sinosoidal wave moves
in a repeating, sinusoidal fashion as a function of time
- The angular wave number k is defined as
k = 2*pi/wavelength
- Partial derivatives involve holding all but a single variable
fixed, and then looking at the effect of small changes
in that one variable
- Taking the partial derivative of a sinusoidal wave equation
with respect to time yields simple harmonic motion
- The power transmitted to a medium of linear mass density "mu"
as a wave passes through it is
Power = 0.5 * mu * omega^2 * A^2 * velocity
This lecture discusses material in Chapter 16 of Serway.