Hambric Vibroacoustic Demonstrators

This demonstrator shows simple propagating and standing waves. Three waves are shown in the plot. Animate them by clicking on the 'start' button under the Animate controls on the bottom right. The top wave is the incident wave which starts on the far left at x=0 and propagates to the right. The middle wave is reflected from a rigid wall on the far right and propagates to the left, back toward the source. The bottom waveform is the sum of the two, which for the default low damping level looks like a standing wave. Although it looks like the wave is stationary, it's actually comprised of the underlying left and right traveling waves.

Change the frequency or speed of the wave with the two sliders on the lower left and watch the waveforms lengthen or shrink. You can also track the wavelength, wavenumber, and dimensionless wavenumber kL in the title. kL is also expressed as a multiple of π, where π represents one half wave along the length L.

Change the damping within the wave with the damping slider. The incident wave amplitude decreases with distance from the origin (hover your mouse over the waveform to track the decay). The reflected wave is also attenuated with distance from the right wall. The most interesting effect is on the summed wave. If you increase the damping substantially the summed wave looks like the propagating incident wave near the source. However, near the right wall the waveform appears to be standing again. This phenomenon is well known in acoustic enclosures, where the sound near a source appears to be propagating, or 'direct field', and the sound far from a source and closer to a wall appears to be standing, or 'reverberant'. Change the frequency, wave speed, or damping to adjust the 'breakpoint' between the direct and reverberant regions of the summed waveform.

At very high frequencies, low sound speeds, and high damping the reverberant field is nearly completely suppressed, and the summed wave simply converges to the incident wave, decaying to nearly zero at the right wall (a free-field). Conversely, at very low frequencies, high sound speeds, and low damping the summed wave becomes completely reverberant.