Number 751 October 26, 2005 by Phillip F. Schewe, Ben Stein
At last week’s meeting of the Acoustical Society of America in Minneapolis, Joel Mobley of the University of Mississippi ([email protected]) argued that even the sound waves (which normally travel about one mile per second in water) could take on superluminal properties. Ultrasound’s group velocity, he said, could jump by five orders of magnitude over its ordinary values and exceed c, when pulses of high-frequency sound strike a mixture of water and tiny (approximately 0.1-mm diameter) plastic spheres. While Mobley has not yet demonstrated this feat experimentally, his preliminary experiments on ultrasound in a water-sphere mixture have shown close agreement with theory and indicate that very large group velocities are possible.
If experimentally confirmed, superluminal group velocity in sound waves could potentially be exploited for useful applications, such as making electronic filters and high-frequency ultrasound oscillators. At this point, it is worth remembering that sound waves–like all waves–are made of two main parts: (1) the underlying wave oscillations, in this case pressure oscillations in a medium such as air or water, which travel at the normal speeds of sound, and (2) the “envelope” that gives the wave its shape. In Mobley’s setup, the envelope has the shape of a bell curve. The speed at which the envelope moves is called the group velocity.
One measures the group velocity by following the envelope’s peak (its maximum height, or amplitude). In a mixture of water and beads, an ultrasound pulse experiences severe dispersion, meaning that different frequencies in the pulse travel at very different speeds. The components of the wave add up so that the peak of the wave can move faster than c. With even greater degrees of dispersion, the peak can actually start traveling backwards, so that a detector deeper in the mixture detects the peak earlier than a shallower detector. This would result in a negative group velocity. None of this violates the principles of causality, since the leading edge of the ultrasound wave still arrives at the shallower detector first and the deeper detector next.
It’s just the peak of the envelope (which determines the group velocity) which would move around in weird ways. In the late 1990s, Mobley and experimental colleagues at Washington University in St. Louis and Mallinckrodt performed initial experimental measurements of ultrasound waves moving through a volume of approximately 100 parts water to one part plastic spheres (Mobley et al., Journal of the Acoustical Society of America, August 1999; and Hall et al., JASA, February 1997).
Mobley estimates that superluminal group velocity would be achieved in a denser collection of beads, namely a mixture of 20 parts water to one part plastic beads. The catch? The severe dispersion required for superluminal group velocity would so weaken the wave that it would become very hard to detect. Still, Mobley has shown mathematically how such behavior can occur, in what may be considered a mixture of 19th-century wave physics and 21st-century ultrasonics with some granular science thrown in. (Movies and much additional explanation in Mobley’s lay-language paper: http://www.acoustics.org/press/150th/Moble y.html.)