The experimental set-up consists of a cylindrical beaker mounted on a vibration exciter powered with a sinusoidal signal from a frequency synthesiser. The equipment is placed on a stone disk mounted on special acoustic absorbers to eliminate the influence of external vibrations. The beaker has an interior diameter of 84 mm and is 20 mm heigh. The fluid used in this series of measurements is water. The water depth is 10 mm. The beaker vibrates at a frequency of 260 Hz, and the amplitude of the driving signal is used as the control parameter in the experiment. The actual amplitude of the oscillations of the container has been measured to depend linearly on the amplitude of the driving signal by Bo Christiansen and Mogens T. Levinsen.
When the forcing amplitude, A, exceeds a critical value, , waves are
formed on the surface. The frequency of the waves, , is half the forcing
frequency. The wavelength, , can be derived from the dispersion
relation, when the wavelength is much smaller than the water depth.
where g denotes acceleration of gravity ( in KÝbenhavn), k denotes the wavenumber, and denotes the surface tension. The wavelength can also be measured from images of the wave patterns formed as described in [3, 8]. The image on the left in figure 2.1 is an example of such an image, but without a ruler. When we measure the wavelength directly from the images, we get the result . Ignoring the g k-part, which only contributes of the right hand side (using the measured wavelength), and using Bo Christiansen's value for the surface tension, we get a wavelength of from the dispersion relation.
Mushroom spores are put on the water surface to visualise the flow. They were chosen because they float on water, and because of their small size. The mushroom spores do give certain problems for studying relative diffusion; they have a tendency to stick to each other when they collide, thus putting a lower limit to the particle separation it is possible to work with. The mushroom spores are hydrophobic. This is a bit of a problem, because it means that they do not float in water (like a buoy). They create a small depression in the water surface and lie on the surface. They are thus not exposed to the motion of the fluid in the same way as a particle inside the fluid.
The particles are illuminated by a DC halogen lamp, and photographed with a CCD camera which sends the images to a video recorder. The lamp shines light on the particles almost parallel to the surface to avoid that reflections and/or refractions from the surface waves disturb the image.
The recording is then replayed at a slower speed, and fed into a PC based frame grabber. The PC processes the sequence of images to a collection of particle tracks. The data processing is described in detail in chapter 4.
The conversion from a digital signal, the CCD output, to an analog signal, in the video recorder, and back to a digital signal, in the frame grabber, is not an optimal method for processing video data. But at the time the experiment was built it was not possible for us to record a digital video signal directly into a computer or onto some digital media.
Figure 2.2 shows a drawing of the experimental set-up, table 2.1 gives details of the equipment used in the experiment, and table 2.2 lists the relevant physical properties of water.
Figure 2.2: Experimental set-up. The scale is not quite true. The actual distance between the beaker and the camera is approximately 1 meter, whereas the diameter of the beaker is .
Table 2.1: Details of the Faraday experiment.
Table 2.2: Physical properties of water at room temperature.