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- Wave Equation
|
(93) |
where for waves on a string:
|
(94) |
- Superposition Principle
|
(95) |
(sum of solutions is solution). Leads to interference, standing waves.
- Travelling Wave Pulse
|
(96) |
where is an arbitrary functional shape or pulse
- Harmonic Travelling Waves
|
(97) |
where frequency , wavelength , wave number
and angular frequency are related to by:
|
(98) |
- Stationary Harmonic Waves
|
(99) |
where one can select and so that waves on a string of
length satisfy fixed or free boundary conditions.
- Energy (of wave on string)
|
(100) |
is the total energy in a wavelength of a travelling harmonic wave. The
wave transports the power
|
(101) |
past any point on the string.
- Reflection/Transmission of Waves
- Light string (medium) to heavy string (medium): Transmitted pulse
right side up, reflected pulse inverted. (A fixed string boundary is the
limit of attaching to an ``infinitely heavy string'').
- Heavy string to light string: Transmitted pulse right side up,
reflected pulse right side up. (a free string boundary is the limit of
attaching to a ``massless string'').
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Robert G. Brown
2004-04-12