Date post: | 17-Jul-2015 |
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Standing WavesPhys 101 Learning Objects
Carly Chui
What is a standing wave?
special case of interference when 2 waves meeting are:
of the same amplitude
of the same frequency
traveling in opposite directions
To demonstrate how a standing wave is created, the following slides show a series of diagrams showing how it happens
by considering 2 transverse waves traveling in opposite directions along a stretched rope
red line = wave 1 moving to the right blue line = wave 2 moving to the left
green line = total
Here, the blue and red line are overlapped, so only the blue line can be seen
red line = wave 1 moving to the right blue line = wave 2 moving to the left
green line = total
Wave 1 moves to the right, while wave 2 moves to the left, while the maximum displacement of the wave is smaller than the previous as
the waves 1 and 2 are not overlapping
red line = wave 1 moving to the right blue line = wave 2 moving to the left
green line = total
As wave 1 and 2 are exactly opposite each other, the total wave is flat (on the x-axis)
red line = wave 1 moving to the right blue line = wave 2 moving to the left
green line = total
Wave 1 and 2 each move to the right and to the left, while the total wave is at its maximum or minimum when waves 1 and 2
intersect.
red line = wave 1 moving to the right blue line = wave 2 moving to the left
green line = total
The waves are overlapped again, giving double the amplitude for the total wave compared to the wave 1 and wave 2.
As a result of the above diagrams, the plot of the total wave (total displacement vs. distance) will be:
nodes = point on the rope that are always at rest
nodes
anti-nodes
antinodes = points where the maximum movements take place
* The three colours (green, red, blue) now correspond to different times. The string oscillates up and down
the resulting standing wave has its name:
its wave pattern remains fixed in space
only the displacement that changes over time
To enhance the understanding towards standing waves, the following compares
it with a normal travelling wave:
all points on the wave have different amplitudes
maximum amplitude at the antinodes, 0 at the nodes
Amplitude
Standing wave: Normal traveling wave
all points on the wave have the same amplitude
Frequency
Standing wave: Normal traveling wave
all points oscillate with the same frequency
all points oscillate with the same frequency
Wavelength
Standing wave: Normal traveling wave
twice the distance from one node/ antinode to the next node/antinode)
shortest distance (m) along the wave between 2 points that are in phase with one another
Phase
Standing wave: Normal traveling wave
all points between one node and the next node are moving in phase
all points along a wavelength have different phases
Energy
Standing wave: Normal traveling wave
energy is not transmitted through wave
BUT - has energy associated with it
energy is transmitted by the wave