A low cost ripple tank experiment with 3D printed components and an Arduino control unit

In this article we present a ripple tank with 3D printed components including a control unit with Arduino microcontroller that can be inexpensively replicated. With the presented setup, experiments such as Huygens’ principle, diffraction, and the double-slit experiment according to Young are possible. Due to the simple operability and the comparatively low price, the experiments can be carried out easily and quickly by the learners themselves.


Introduction
The ripple tank is a key experiment to show wave phenomena such as Huygens' principle, diffraction, refraction and reflection.Corresponding experiments for investigating water waves were described, for example, by Tyler as early as 1936 with a comparatively complex setup [1].For many years, there have been commercial, comparatively expensive ripple tank sets for the educational sector, which are usually to be conducted by the teacher as a demonstration experiment.Therefore, there is a need for inexpensive variants with which high-quality experimental results can nevertheless be achieved.Various approaches have already been published: Thy and Iwayama, for example, analyse the results of the ripple tank with a smartphone and tracker [2].Thepnurat et al build a DIY ripple tank whose frequency generator is controlled by a smartphone [3].
In this article, a low cost version of the ripple tank is presented, that consists of 3D printed components and an Arduino control unit.With it, highquality representations of wave patterns of various phenomena can be achieved.The concept is designed for the simplest and most intuitive operation possible, so that the experiments can also be carried out by the learners themselves in student experiments.

A brief theory about waves
Waves and their phenomena play a decisive role in various subject areas such as mechanics, acoustics, electromagnetism and also quantum physics.The classic waves include transversal, longitudinal waves or torsional waves (a hybrid of transversal and longitudinal waves).A distinction is made between longitudinal waves and transversal waves based on the direction of vibration of the individual oscillators and the direction of the propagation of the waves in relation to one another.
In the case of mechanical longitudinal waves such as sound waves, the direction of vibration of the individual oscillators and the direction of propagation of the wave are the same.In contrast the direction of vibration of the individual oscillators and the direction of propagation of the wave of a mechanical transversal wave such as water waves in the ripple tank or also in vibrating guitar strings, run perpendicularly to one another in a highly simplified manner (there are different types of water waves).In the case of mechanical transversal waves, we can speak of wave crests and wave troughs (figure 1).The wave itself is characterized by the amplitude A 0 and the wavelength λ (figure 2).The wavelength λ is the distance between two successive identical points of a wave, while the wave period is the time required for a complete oscillation of a wave.The wavelength λ is measured in spatial units, while the wave period is measured in temporal units.In general, the propagation of homogeneous, two-dimensional waves in the form of water waves can be displayed and analysed with a ripple tank.Various experiments can be carried out by using different exciters (e.g.point, multiple point and paddle) and obstacles (on the water surface: gap, wall, double gap or in the water: transparent block).
To make the phenomenon visible, light is usually directed through the medium of water onto a projection surface.In the very much simplified model in figure 3, parallel light shines from above through the tub with water onto the projection surface below.The oscillator creates water waves with crests and troughs.
The light of the illumination converges through the crests and diverges through the troughs of the water surface similar to convex and concave lens do, see figure 3.This creates either a scattering or a collection of the light rays.As a result, the light rays result in dark and bright areas on the projection screen through diacaustic.

A 3D printed low cost ripple tank
The ripple tank presented here consists of 3D printed parts as well as simple standard parts (e.g.plastic box, screws and nuts) and electronic components.Due to its simple principle and the low price, it can also be produced and used in larger numbers as a student experiment.Furthermore, during the design, care was taken to ensure that it can easily be maintained and repaired.The parts can be dismantled and-if necessary-reprinted.The colour concept was developed for the traceability and understanding of the experimental set-up.The individual components are printed in different colour filaments.This serves as a link between the components and their operation and thus offers the possibility of visually assigning the respective properties to the components.For example, the lighting component is made of yellow filament, as is the button for adjusting the lighting frequency on the control element.Likewise, the button for varying the frequency of the coil is printed in red, like the coil itself.
The structure (figure 4) consists of the frame and tray (a), the exciter (b), the light (c) and the control unit (d).Various inserts (e) and attachments (f) can be mounted on the exciter.
(a) The frame (black tripods) encloses the tub (a plastic box) from two sides and supports it at a height of 90 mm above the table surface.The frame can be dismantled with screws and can thus be adapted to the shape of the tub (any size between 150 mm and 190 mm) and at the same time stowed away to save space.(b) The central element of the ripple tank is the exciter (see also figures 5 and 6).This consists of the movable stamp base (green), the body with the internal magnetic slide, the coil (red) and the guide rail with height adjustment and slot for attachment to the rail.Its function is to cause the water surface to vibrate.The individual components were printed in different colours so that the structure of the exciter is as understandable as possible for the learners.In this way, the relation and tasks of the components can visually be captured.The corresponding controls of the control unit are designed in the same colours (d).During operation, the magnetic slide with inserted neodymium magnets (green) is pushed into or out  of the coil in the body (grey) by the changing magnetic field of the coil (red).A spring is inserted above and below the carriage for damping (figure 6).This creates an oscillating movement that is transmitted to the water surface via the rod and the exciter foot.The foot of the exciter must be directly at the height of the water surface.A fine adjustment of the height can be made using the adjusting wheel (light blue), which holds the body together with the carriage unit vertically in the guide rail (blue).
(c) The lighting is attached at the side directly next to the exciter.The LED is placed over the tub to illuminate the area of the table below the water tub.The lighting can be operated in two modes: besides permanent lighting, stroboscopic lighting can also be set.The frequency of the LED is linked to the frequency of the stamp base.This results in the projection of a stationary wave pattern on the table.(d) The ripple tank can be operated with a conventional frequency generator or an inexpensive control unit consisting of an Arduino with an amplifier.The frequency and amplitude of the exciter can be regulated, as well as an optional frequency difference between the frequency of the lighting and the frequency of the wave generator.This is shown on the liquid crystal display.(e) The inserts can be placed on the edge of the tub and pushed along the long side.If necessary, the exciter and the lighting must be aligned in the middle of the inserts.(f) The attachments can be plugged into the foot of the exciter and thus enable easy (dis)assembly and easy replacement.
The total cost of all components on figure 4, including printed parts, is around €40.A list of materials as well as the required 3D print files, circuit diagram and program code are available as a free download on https://physikkommunizieren.de/3d-printed-ripple-tank.

Experiments with ripple tanks
Various fundamental wave phenomena can be represented with ripple tanks.In the following, three classical (famous) phenomena as well as their realisation and results with the low cost ripple tank and the Arduino control unit are presented as examples.In addition, students can also design, print and test their own inserts.

Principle of Huygen
The Dutch physicist Christiaan Huygens' developed a fundamental wave theory in 1678.His theory is based on a geometric method that allows the position of wave fronts to be calculated as a function of time.This is summarized in Huygens' principle: 'Every point of a wave front is the starting point of a new spherical elementary wave.A wave front results from the superposition of several elementary waves' (see figure 7).

Realisation in the experiment
The basic setup with the attachment 'multiple sources' is required for the experimental setup, which looks like a wide comb.The insert is clamped to the bottom of the stamp base and adjusted to the level of the water surface (figure 8).As a result, the following wave pattern can be observed below the tray (figure 9).

Diffraction
Diffraction describes the phenomenon that occurs when a wave hits an obstacle in which there is an opening.Only part of the incoming plane wave gets through the opening.Behind the opening, the wave spreads out in a circle in the edge areas-this part of the wave is 'diffracted' (depending on the ratio of the size of the opening to the wavelength).This phenomenon can also be explained using Huygens' principle: new elementary waves are formed in the gap and propagate in all directions.Figure 10 shows the diffraction of waves behind a wall with a slit.Here you can clearly see the diffraction of the initially plane wave to form a circular wave.An essential feature of the phenomenon is: the narrower the slit, the more the incident wave front is diffracted and the more the wave spreads out in space behind the split.From this it can be deduced that the laws of geometric optics only apply if the openings (e.g. the slit) are significantly larger than the wavelength of the light.

Realisation in the experiment
For the experimental set-up, the basic set-up with the attachment 'plane wave' is required.This is clamped to the bottom of the stamp foot and adjusted to the height of the water surface.In addition, an obstacle with a gap is placed on the edge of the tray (figure 11).As a result, the following wave pattern can be observed below the tray (figure 12).

Young's double-slit experiment
In 1801, the scientist Thomas Young first demonstrated the wave properties of light.He showed the interference behaviour of light and drew conclusions about waves in general.The principle of the experimental setup known as 'Young's doubleslit experiment' is shown in figure 13.If a wave hits an obstacle with a gap, a circular wave is created behind the obstacle (Huygens' principle, see above).If these waves hit an obstacle with two openings, two punctiform waves are created, which now interfere with each other.In a similar case of light interference, the individual maxima and minima can be observed and appear as bright (constructive interference) or dark (destructive interference) areas.

Realisation in the experiment
With the setup different variants of the double-slit test can be implemented.The circular wave exciter with a double-slit insert or a dual exciter delivers  good results (figure 14).With the latter, the result can be seen more clearly (figure 15).

Conclusion
With the material presented here, all experiments of a 'regular' commercial ripple tank are possible at a fraction of the price.Depending on the ambient light conditions, the representation of the phenomena on the table surface is not always quite as clear as that of a conventional ripple tank in the demonstration experiment.However, as a low cost experiment, this ripple tank can be set up on the table, directly in front of the students in small groups, and can be operated by them themselves.The students are therefore much closer to the phenomenon and can thus also observe and experi-ence the subtleties more easily.A sheet of paper can be placed under the tray, onto which the visible experimental results can directly be created as a drawing (in stroboscopic mode).The possibility to conduct an experiment by yourself, to influence the representation of the phenomenon and to get a haptic, three-dimensional impression of the structure also make a clear difference to digital alternatives (e.g [3]).Our studies showed the suitability of the material to be used in experiments by both students (future physics teachers) and pupils (aged 15-19).The colour scheme helps to better understand the relation between the components and the control.

Figure 2 .
Figure 2. Graphic representation of the mathematical quantities of a wave.

Figure 3 .
Figure 3.The highly simplified principle of light refraction by water waves.

Figure 6 .
Figure 6.General view (left) and cross-section view (right) of the exciter.

Figure 9 .
Figure 9. Wave pattern of Huygens' principle.On the right-hand side of the image, the contours of the individual point waves can be seen.In the course of the image to the left side, the individual point waves interfere to form a plane wave.

Figure 10 .
Figure 10.Simplified diffraction of water waves at slit.On the left, a plane wave runs against an obstacle with a small opening.The waves spread out in a circle behind the obstacle.

Figure 11 .
Figure 11.Setup for the experiment 'diffraction at the slit'.

Figure 12 .
Figure 12.Resulting wave pattern in front and behind the slit.

Figure 13 .
Figure 13.Young's double-slit experiment: with incident plane water wave; a wall with two openings and the resulting interference pattern.

Figure 14 .
Figure 14.Structure of the experiment 'combination of two circular waves, interference'.

Figure 15 .
Figure 15.Wave pattern of the experiment 'combination of two circular waves, interference'.