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In the theory, the authors included nearest-neighbor ͓ 20 ͔ and second-nearest- neighbor ͓ 21 ͔ interactions, which we will discuss below. Fourth, the dust charge Q was determined in previous experiments with Mach cones ͓ 20,21 ͔ by measuring the sound speed from the cone angle and comparing to the sound speed predicted by the theoretical dispersion relation for a 2D DLW assuming a Yukawa potential. These methods use a dispersion relation that assumes a Yukawa interparticle potential. In recent experiments with a linear chain ͓ 28 ͔ both Q and ␬ were measured simultaneously by fitting the dispersion of the DLW. The first authors to use this method ͓ 12,13 ͔ employed the resonance method to measure Q. A third method involves comparing experimentally measured and theoretical DLW dispersion relations to provide a measurement of ␬. The parameters are determined by fitting the particle orbits in a center-of-mass frame. This method is limited to use with a suspension of two particles that can be made to collide. As a second method, binary collisions were used by Konopka et al. The method assumes that the electric potential profile in the sheath is parabolic. The method also requires a value for the ion density in the sheath, which must be extrapolated from Langmuir-probe measurements made in the bulk plasma region. The vertical resonance frequency can be measured with high precision. Particles are shaken in the vertical direction by modulating the voltage on the lower electrode. The first method was the resonance technique 6,26, which is based on the force equilibrium between electric field force and gravity. Then, we will present several new methods that we have devised, based on the sound speed measured from Mach cones. Various methods have been developed to measure them, which we review next. The particle charge Q and the screening strength are crucial parameters in the determination of the crystal prop- erties. We will exploit our ability to measure sound speeds at two different number densities in the next section, yielding a measurement of the screening strength and, consequently, the particle charge.

This is expected, since the spring constant increases when the crystal is more compressed. 10 it is seen that at a higher number density, the sound speed is faster. That is because the plasma is produced by the electrode, which has a much larger diameter than the suspension of microspheres. While the number density varies from the center to the edge of the particle cloud, we believe the plasma conditions and therefore the charge do not. As mentioned in the Introduction, the number density is highest in the center and lower at the edge, corresponding, for example, to experimental conditions I and II, respectively. Here, the Mach cones have been excited under the same discharge conditions, but in different parts of the crystal cloud, in the center and at the edge. A useful test of the dependence of the sound speed c on the particle number density is shown in Fig. of Peeters and Wu ͓ 18 ͔ predicts that the compressional wave is five times faster than the shear wave, for ␬ ϭ 1.