Standing waves on a string occur when two identical waves travel past each other in opposite directions.
(This happens when a wave sent down the string from one end reflects at the other end and comes back again.)
In the simulation,
the wave in the top panel is described by f(x,t) and travels to the right. The wave g(x,t) in the middle panel
is identical to f(x,t) except for its direction
of travel, so it travels to the left. The superposition of f(x,t) and g(x,t) is just the sum of those two waves at
every point, and that superposition is the standing wave shown in the bottom panel.
Let n represent the number of half-wavelengths that 'fit' onto the string. Click on a blue link to see the f(x,t) and g(x,t)
that are added together to produce the standing wave pattern that has n antinodes.
This simulation is a lot like an actual experiment we can set up in the classroom (and will use for our lab). Click through the
links to observe the different standing wave patterns that correspond to different 'modes' of vibration.
In your own words, try to describe what is being done here in order to change from one mode of vibration to another.
- What stays the same from mode to mode?
- What changes as you go from mode to mode?
(Hint: Consider things like the speed, wavelength, frequency, and amplitude of the waves f(x,t) and g(x,t).)