![superluminal group velocity superluminal group velocity](https://www.askamathematician.com/wp-content/uploads/2010/10/000.jpg)
“Consider the pulse speed in a slightly less dramatic case,” Robertson said. It might not seem that a negative velocity would exceed the speed of light, but in this case, Robertson said, the speed of the pulse is actually much faster than c. “Using the definition for speed as being equal to distance divided by time, we measured a negative time and thus realized a negative velocity.” “We also achieved what is known as a ‘negative group velocity,’ a situation in which the peak of the output pulse exits the filter before the peak of the input pulse has reached the beginning of the filter,” explained Robertson. With this experiment, the group velocity could actually reach an infinitely small amount of time, although the individual spectral components still travel at the speed of sound. The 0.65-meter loop split the sound waves into two unequal path lengths, resulting in destructive interference and standing wave resonances that together created transmission dips at regular frequencies.ĭue to anomalous dispersion (which changes the wave speed), sound pulses traveling through the loop filter arrived at the exit sooner than pulses traveling straight through the PVC. To rephase the spectral components, the sound waves were sent through an asymmetric loop filter on a waveguide of PVC pipe, about 8 m long. By appropriate phase manipulation (rephasing) the group velocity can be increased or decreased.” “The sound-faster-than-light result will not be a surprise to the folks who work closely in this area because they recognize that the group velocity (the velocity that the peak of a pulse moves) is not merely connected to the velocity of all of the frequencies that superpose to create that pulse,” explained Robertson, “but rather to the manner in which a material or a filter changes the phase relationship between these components. So it’s not the actual sound waves that exceed c, but the waves’ “group velocity,” or the “length of the sample divided by the time taken for the peak of a pulse to traverse the sample.”
![superluminal group velocity superluminal group velocity](https://i.stack.imgur.com/6N935.jpg)
In their experiment, the researchers achieved superluminal sound velocity by rephasing the spectral components of the sound pulses, which later recombine to form an identical-looking part of the pulse much further along within the pulse. The grant aims to increase recruitment and retention of students to these subjects. The experiment was conducted by two undergrads, an area high school teacher and two high school students, who received funding by an NSF STEP (Science, technology, engineering, math Talent Enhancement Program) grant. Using sound to create a group velocity that exceeds the speed of light is significant here because it dramatically illustrates this point, due to the large difference between the speeds of sound and light.” “Phase manipulation can change the phase relationship between these materials’ components. “All of the interest in fast (and slow) wave velocity for all types of waves (optical, electrical, and acoustic) was initially to gain a fundamental understanding of the characteristics of wave propagation,” Robertson told. But while the individual spectral components of these pulses have velocities very close to c, the components of sound waves are almost six orders of magnitude slower than light (compare 340 m/s to 300,000,000 m/s). Past experiments have demonstrated that the group velocities of other materials’ components-such as optical, microwave, and electrical pulses-can exceed the speed of light.