The same notes, the same clock, different media. Look along the acoustic path and compare air, water, and their boundary. Select one, two, or all three worlds.
Select a world above to see and hear it. Visual time is retained.
Place the same rigid object in every world. Try moving it across the colored paths while listening. Opening a near or far face lets waves enter; a top opening runs parallel to these waves.
Bright peach outlines mark rigid faces; Dashed note-colored curves are box reflections. Each colored lane is a separate axial pressure sample, monitored at the marked probe depth. Moving a face changes interference and the audible mix. This is an axial ray approximation: no edge diffraction, side-wall scattering, or full room reverberation. Up to four boundary encounters are traced; late echoes are omitted. Small objects compared with a wavelength need a fuller wave solver.
Air sources exist in the air and mixed worlds; water sources exist in the water and mixed worlds. Enabling both adds their coherent fields. A disabled emitter produces no waves.
Listening switches mute the corresponding monitors, not the emitters or the transmitted waves. Only visible worlds contribute audio. In the mixed world, air and water probes are panned left and right.
Fractions apply to each incoming plane wave separately. Equal source levels mean equal incident intensity per note. Traces and audio use pressure divided by sqrt(impedance), so amplitudes can be compared without mistaking high water pressure for extra transmitted energy.
The receiving wave keeps its frequency. Wavelength and travel time change. Dashed curves are reflected components; solid curves are incident or transmitted components. These are pressure graphs laid out in perspective, not sideways motion of the fluid. The boundary is drawn as a window normal to the viewing axis, not as an ocean surface viewed from shore.
Enable sound to see the measured output.
Each note is monitored on its colored lane. Each monitor includes the coherent incident, reflected, and transmitted contributions that reach it. Audio uses physical propagation delays and normal musical pitch; the visual clock is slowed independently. Fixed mix headroom avoids boosting a quiet transmitted signal when another monitor is muted.
Linear, lossless plane waves at normal incidence between two ideal fluid half-spaces. Approximate material values near 20 C: air density 1.204 kg/m^3, sound speed 343 m/s; water density 998.2 kg/m^3, sound speed 1482 m/s. The finite drawing shows part of the field, not reflecting tank walls. Box faces are ideal rigid reflectors with pressure reflection +1 and zero transmission. Only faces normal to the viewing axis intercept the modeled rays. The surrounding fluid stays the same inside an open or closed box; this does not model a sealed air pocket underwater. There is no absorption, cavitation, surface-wave simulation, diffraction, oblique refraction, or spherical spreading.
Z = density * sound_speedr_pressure = (Z2 - Z1) / (Z2 + Z1)t_pressure = 2 * Z2 / (Z1 + Z2)R_energy = r_pressure^2T_energy = 4 * Z1 * Z2 / (Z1 + Z2)^2R_energy + T_energy = 1q = pressure / sqrt(Z)q_transmitted / q_incident = sqrt(T_energy)wavelength = sound_speed / frequencyq(z,t) = sum(path_gain * sin(2*pi*frequency*(t - path_delay)))
The near air source is at path coordinate 2 m and points forward; the far water source is at 26 m and points back. Air and water probes are at 7 m and 19 m. Opposing sources share an oscillator reference for each note, with equal source phase. The drawing and audio represent steady-state fields; source startup envelopes are not simulated. Wave markers indicate propagation direction. Appearance toggles never alter the calculated reflection or audio.
Audio is a normalized sonification, not a calibrated underwater listening experience or simulated human hearing. Muting all probes, hiding all worlds, disabling both emitters, or clearing notes silences the mix. Changing visible worlds preserves visual time.
References: UNSW: acoustic impedance and intensity; Stanford: reflection and transmission.