Masters Thesis: Ripple Tank and Acoustic Analogue

The Masters Thesis: Ripple Tank and Acoustic Analogue. The Ripple Tank is a classic method to visualize wave propagation. This book is the written thesis which accompanied the physical ripple tank system I developed for the master’s degree in mechanical engineering at Cal State University at Long Beach in 1975. The requirement was to make a roll around classroom ripple tank demonstration cart, self contained and capable of replicating the wave propagation examples found in the textbook: Fundamentals in Acoustics, Kinsler and Frey, 1950, Wiley & Sons.

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Chapter 1

This chapter describes the construction and operation details of the ripple tank system developed to complete this thesis. This model ripple tank had a nearfield projection screen of ground glass suspended directly over the apparatus. This was useful when setting the demonstration up and for small group observing. By moving the translucent screen aside, the wave movement was projected onto the ceiling above the apparatus in a darkened classroom.

Two types of image illumination were used. The more traditional slide projector provided a view of the wavefield, similar to that seen when watching ocean waves moving towards the shore from a high location. A second type of illumination utilized a GE 1531 Strobotac which enabled viewing of wave fronts as they appear to be frozen is space. Slight adjustments in the stroboscope timing allowed the appearance of the wavefronts to slowly move forward or backwards. The Strobotac cast a bright white image while the slide projector cast a slightly brownish image. Both light sources could be turned on and both the wavefield pattern and the frozen wavefront images could be viewed at one time. When looking at propagating waves, it is possible to watch either the wavefront or the wave field but only one at a time. By simultaneous illumination of the wave field by strobe and steady light, both can be seen at one time.

The bottom of the ripple tank was a sheet of flat glass. Below the ripple tank was a large optically flat mirror set at an angle of 45 degrees. It was interesting how difficult it was to find a flat mirror. To demonstrate a mirror was flat it was taken outside and reflected the sun onto the distant wall of a building, hundreds of feet away. Most all readily accessible mirrors produced distorted sunlit images at a distance. Eventually an antique mirror was discovered which produced an optically flat reflection, and was used in the Ripple tank.

The traditional ripple tanks used floating dowels on which a motor with a rotating eccentric weight. This produced waves with substantial “harmonic distortion” which appeared as smaller wavelength higher frequency ripples traveling along with the main waves. Ripple wave speed varies with wavelength, and so we end up with waves on top of waves and a very unclear viewing field. A cleaner waves source was needed, one whose frequency could be varied without the introduction of upper partials.

The face of a small loudspeaker was covered over with a wood plate, all except for a small opening in the middle, into which a small pipe was inserted. The speaker was connected to a signal generator that operated in the range between 1 and 10 Hz. Over the open end of the ¼” diameter pipe was slipped a flexible hose, whose other end was plugged into a funnel. The open end of the funnel was suspended over the water so it’s lip was just barely in contact with the water surface, essentially the seal was maintained by the surface tension, the meniscus of the water. When a low amplitude oscillating signal was applied to the speaker, water level moved up and down creating an expanding ring of waves, free from any distortion. The frequency could be easily varied. The frequency signal could be sent into the strobotac and the strobe would flash at the same phase of each cycle. This system proved to be a very dependable system.

Once a set of waves were created, they reflected off the flat walls of the ripple tank, resulting in a reverb chamber effect. What was needed is a reflection free wall system, more like an anechoic chamber. A miniature “beach” for water ripples was created by adding a shallow sloping floor section around the perimeter of the tank that was faced with 3M 96 Scouring Pads.

Chapter 2

Here I discuss a formal proof that ripple tanks do model wave behavior using fluid mechanics similitude modeling equations. Derived is the wavelength and frequency and wave speed equation, also Mach and Froud numbers. Also provided is the traditional wave equation derivation that usually is used to compare water ripple waves to soundwaves. Further, with ripples the wave speed varies with frequency and water depth while not so with acoustic waves. Finally, the ripple wave speed is shown to become constant for water depth under ¼”.

Chapter 3

This is a dedicated focus on the Helmholtz Resonator. The ¼” wave depth only works for wave field demonstrations. When trying to demonstrate lumped parameter modeling of wave behavior, when the object size is less than ¼ wavelength, the water meniscus effect becomes too great for effective modeling. Deep water is needed to demo lumped parameter acoustic effects and this is derived. The Helmholtz resonator is also applied to waves in ducts, in this case water channels to demonstrate the sound cancel effect.

Chapter 4

Finally I explore the distributed impedance of waves in channels. Distributed inertance and compliance is developed for the rectangular channels and then for a number of other channel cross sections, this leads to standing waves and channel filter networks.

• Appendix A is a comprehensive graph of frequency, wavelength and wave speed for ripple tank water depths.
• Appendix B contains operational notes covering cleaning and water treatment for clear visibility