- 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

- Viewgraph 14
- Viewgraph 15

Note that the energy deposited by this wave depends on several of its properties, and in different ways.

- the energy increases as the
**amplitude squared** - the energy increases as the
**frequency cubed**

Joe sings into a long cardboard tube of radiusr = 0.2 m. He hits a perfect middle C (256 Hz), causing the air molecules to shake back-and-forth. At the far end of the tube, the sound wave carries a power of0.01 Watt = 0.01 Joule/sec. How large is the amplitude of motion of the air molecules in the tube?