4.5 STANDING WAVES
can be defined as
The principle of superposition yields a surprising sum for two identical waves traveling in opposite directions.
for example:
The black wave is the resultant wave (standing wave) of the interference of the travelling blue and green wave
Diagram 1.0
are different from travelling waves because (refer to Diagram 1.0)
1) the crests stays at the same place
2) nodes- from destructive interference, displacement = 0
3) antinodes - from constructive interference, max displacement
4) points between consecutive nodes are in phase, have a same direction of velocity
5) poinst in-between next pair of consecutive nodes have a opposite velocity direction
6) the maximum amplitude of oscillation is different at different points
7) does not transfer energy since it does not move
have two types of boundaries which are
Standing waves on strings
Standing waves in pipes
occurs when
occurs when
Waves travel to the ends of the string and reflect at each end, and return to interfere under precisely the conditions needed for a standing wave
the formulas for n harmonic (note that length equals to half the wavelength)
the equation
to calculate the wavelength in the condition
when one end free and one end fixed, node-antinode
(n=1,2,3...):
when both ends fixed or both free,
node-node or antinode-antinode (n=1,3,5...):
to calculate the frequency is
Longitudinal waves are created (instead of transverse waves), and these waves are reflected from the ends of the pipe #
for example: a guitar
for example: a flute
than can be in a condition of
antinode-node (close end pipe)
antinode-antinode (open end pipe)
that can be in a condition of
node-node (both fixed end)
antinode-node (one free one fixed end)
because
the number of nodes and antinodes are equal
because
the number of nodes and antinodes differ by 1
for example at 1st harmonic,
for example at 1st harmonic,
for example at 1st harmonic,
for example at 1st harmonic,