Wave Propagation Between Reflecting Boundaries

Resonances and Standing Waves

Reflectivity: Reflectivity:




Periods: /4


Pulse Width:

Sine Wave Pulse Train Single Sine Single Pulse
Wave Function Pressure Forward Backward Particles

Open Educational Animation, created by W. Kausel
Department of Music Acoustics (Wiener Klangstil, iwk.mdw.ac.at)
mdw - University of Music and Performing Arts Vienna
Anton von Webernplatz 1
1030 Vienna, Austria

Modify excitation position (Pos), excitation force (Magnitude), frequency (quarter periods in resonator), number of harmonic components (Harmonics) and the pulse width (Pulse Width) using the sliders below the animation. All sliders are sensitive to mouse and keyboard input (arrow keys, page up/down, home, end).

Adjust boundary conditions (Reflectivity) using the sliders left and right of the animation (these sliders can also be centered using the "0" key). A reflectivity of 0 corresponds to anechoic conditions. Reflectivity of -1 is linked to a fixed end (a rigid wall). Reflectivity of 1 corresponds to a free end (the open end of a tube).

Excite continuously by a Sine Wave or a Pulse Train or transmit single pulses from the position of the excitation. Be aware that excitation in a node of a standing wave wont excite it much. Therefore avoid reflectivity of -1 at the excited end.

Excitation can be a sine wave with a given number of harmonics or a pulse train with pulses of a given pulse width. Single wavelet or pulse excitation can be selected, too.

Choose and combine the kind of plots using the check boxes below. Wave functions can be decomposed into a forward travelling and a backward travelling partial wave. Pressure is a color coded visualisation of a corresponding longitudinal wave. A longitudinal wave can simultateously or alternatively also be visualised by oscillating air particles.

Restart simulation after parameter changes.

add parameters: .../WaveAnimation?position=200&magnitude=0.1&particle=1

particle precision "pprec=0|1" (square or round particles, affects performance, default = 0)

particle size "psize=1..12" (in pixels, default = 5)

particle displacement "pdispl=1..10" (relative particle displacement amplitude)

particle density "pdensity=0..1" (relative particle density, affects performance, default = 1)

position slider "position=1..600" (excitation position, default = 0)

left reflectivity slider "leftend=-1..1" (reflectivity conditions at left end, default=1)

right reflectivity slider "rightend=-1..1" (reflectivity conditions at right end, default=1)

speed slider"speed=1..10" (relative animation speed, default=5)

magnitude slider "magnitude=0.0025..0.5" (relative excitation force, default=0.05)

wave length slider "quarterperiods=1..60" (quarter periods between reflecting boundaries, default=12)

harmonics slider "harmonics=1..20" (number of harmonic components of excitation signal, default=1))

pulse width slider "pwm=0.01..0.5" (pulse ratio of excitation pulses, default=0.5)

radio button Sine Wave "sinus=0|1" (select continuous sinosoidal excitation, default=1)

radio button Pulse Train "pulses=0|1" (select continuous pulse train excitation, default=0)

radio button Single Sine "sngsinus=0|1" (select single wavelet excitation, default=0)

radio button Single Pulse "sngpulse=0|1" (select single pulse excitation, default=0)

plot Wave Function "wave=0|1" (default=1)

plot Pressure wave "pressure=0|1" (default=0)

plot Forward Wave "forward=0|1" (default=0)

plot Backward wave "backward=0|1" (default=0)

plot Particle wave "particle=0|1" (default=0)