Circular Standing Waves

Standing waves have stationary nodal and antinodal patterns.

Discussion

When waves in a ripple tank are confined by reflecting boundaries, here a metal ring placed in the ripple tank, they may interact to establish standing waves. Standing waves on a string or wave demonstrator are one dimensional, and nodes and antinodes are points; waves in a ripple tank are two dimensional, and nodes and antinodes are not points, but curves. It is found that standing waves are possible only for certain resonant frequencies. In this set of movies waves generated by a point source located at the center of the metal ring interact with waves reflected by the ring. At resonant frequencies these interactions result in standing circular waves. Here, waves are generated by a point source in the center of the circular barrier. Notice that there are no waves outside the barrier.

Unlike ripple tank images of traveling waves, where bright regions result from wave crests acting as converging lenses, the bright rings in images of circular standing waves in a ripple tank are formed by stationary antinodal rings, which alternate between wave crests acting as converging lenses that focus light and wave troughs that act as diverging lenses that spread light. Each bright ring flickers because of this alternation of crests and troughs. The dark rings in images of circular standing waves are the result of the lensing effects of adjacent antinodal rings, which results in reduced light intensity for nodal rings.

With waves in a ripple tank, fixed nodes at boundaries, such as those on a string that is fixed at one or both ends, are not possible. As a consequence, in these movies the outermost bright ring at the edge of the ring is an antinode. The bright spot at the center (the location of the wave driver) is also an antinode. The wavelength of a standing wave in these movies can be calculated using the expression λ = D/(N-1), where N is the number of antinodes, including the ones at the center and edge of the ring, and D is the inside diameter of the ring, 0.148 m. With the wavelength and the frequency of the standing wave, you can calculate the wave speed (v = ƒλ) of ripples in the tank. You can fill in the following table and calculate wave speeds wave speeds. Calculated velocities are consistent with ripple tank wave velocities measured for the depth used.