1.
Standing Waves
Phys 101 Learning Objects
Carly Chui

2.
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

3.
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

4.
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

5.
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

6.
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)

7.
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.

8.
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.

9.
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

10.
the resulting standing wave has its
name:
its wave pattern remains fixed in
space
only the displacement that
changes over time

11.
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

12.
Frequency
Standing wave: Normal traveling wave
all points
oscillate with
the same
frequency
all points
oscillate with
the same
frequency

13.
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

14.
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

15.
Energy
Standing wave: Normal traveling wave
energy is not
transmitted
through wave
BUT - has
energy
associated
with it
energy is
transmitted by
the wave