The fundamental and higher harmonic resonant characteristics of a straight channel with blocked ends is easily accomplished with the water wave system. Its behavior is analogous to that of sound waves in a pipe or a room and to the Kundt tube experiment. It also demonstrates the behavior of a vibrating string, including the absence of particular harmonics due to the location where the plucking occurs.
The water tray is filled to a depth of 1 in. with clean tap water and in it is assembled a 1 in. wide by 12 in. long channel with blocked ends. It is orientated so that the 3/8 by 1 in. wave driver while fixed to the movable platform can be smoothly positioned anywhere along the channel as illustrated in Figure 15. The opening of the wave drive is initially set 1/4 in. below the mean water level and carefully raised or lowered to provide maximum wave image clarity during operation. Generally, the higher the frequency the closer to the mean water level the opening of the wave drive will be set. The wave action will be particularly visible when illuminated by a frequency synchronized Strobotac positioned 15 to 20 feet away while the room lights are darkened.
Nodes and Antinodes
The wave drive is positioned at one end of the channel and its frequency slowly increased from zero. The fundamental resonance mode of vibration will occur at 0.8 Hz. Alternating high and low water levels will appear as corresponding broad and narrow splays of light on the viewing screen as indicated in Figure 16. The viewing screen is initially set about 1 foot above the water surface and raised or lowered for increased focus. The wave peaks and troughs correspond to the minimum and maximum density phases of acoustic resonance and are associated with its standing wave nodes.
As the wave drive is slowly moved along the channel length, two other positions of notable resonance behavior are found: one at midpoint, which is its antinode position, and the other being the far end where the initial response is repeated. The midpoint response of the relatively still water shows the antiresonant consequence of stimulating a vibrating system at its nodal position, i.e., analogous to harmonic absence due to pluck position on the string. Resonant and antiresonant characteristics of each successive harmonic vibration mode can be generated and observed through the sixteenth harmonic.
The antinode and resonance stimulation location of any harmonic (n = 1, 2, 3, . . . ) lies along the channel length (L) at a distance (lm) from either of its ends.
The node and antiresonant stimulation position of any harmonic (n) lies along the channel a distance (lm) from either end given by
These antinode and node locations correspond to those identified as “nodes and loops” by Strutt [Lord Rayleigh] (1945) in his discussion of the Kundt tube and also that covering harmonic absence and pluck position of a string.
Wave Speed Consistency
The condition of standing wave resonance within a tube is easily identified. It is frequency sensitive, which renders it useful for determining the wavelength, λ, of some arbitrary frequency by measuring the tube or channel length (L) and counting the number of nodes (n).
For any given frequency the wavelength determined from the standing wave resonance has been found to differ from that existing in open space of air depending on the physical dimensions and material of the tube (Kinsler and Frey, 1950).
Anticipation of similar results with the water wave system led to a comparison of open field and channel wavelengths throughout the frequency range of 1.5 to 15.0 Hz. The channel width was 1 in. and water depth was 1 in. Open field wavelength was accomplished by direct measurement of its Strobotac “frozen” image while channel wavelength was determined from channel length and number of nodes. The graph of resulting values are on Figure 17 and show no apparent deviations between the two wave systems.
Only blocked channel resonance is considered in this section. The characteristics of a channel with one end blocked and the other open should be investigated and related to the acoustic organ pipe resonance. The termination of the open end also affects the frequency response of an acoustic pipe (Kinsler and Frey, 1950:206) and a comparison of that effective inertial length difference might be detectable with the ripple system.
A variation of the open-ended tube is a horn. The conical, catenoidal and exponential horns have characteristically different frequency response curves for the acoustic system (Morse,1948:283) which ought to be apparent with the ripple analog.
An open field acoustic experiment where the standing wave pressure nodes are determined for various frequencies between an unbaffled speaker that is squarely facing a wall a few feet away conducted by the author shows the speaker to be a velocity or displacement source at the higher frequencies but tends to become a pressure type wave source at the lower frequencies. The relationship between the speaker type wave source and the ripple wave source should be developed.