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- Wave Equation
 |
(10.1) |
where for waves on a string:
 |
(10.2) |
- Superposition Principle
 |
(10.3) |
(sum of solutions is solution). Leads to interference, standing waves.
- Travelling Wave Pulse
 |
(10.4) |
where
is an arbitrary functional shape or pulse
- Harmonic Travelling Waves
 |
(10.5) |
where frequency
, wavelength
, wave number
and angular frequency
are related to
by:
 |
(10.6) |
- Stationary Harmonic Waves
 |
(10.7) |
where one can select
and
so that waves on a string of
length
satisfy fixed or free boundary conditions.
- Energy (of wave on string)
 |
(10.8) |
is the total energy in a wavelength of a travelling harmonic wave. The
wave transports the power
 |
(10.9) |
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'').
Next: Waves
Up: The Wave Equation
Previous: The Wave Equation
Contents
Robert G. Brown
2008-01-29