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Wave Physics

Boundary Impedance Reflections & Doppler Effect Simulator

Media Boundary Parameters

Medium 1 (Incident Side)
°C
%
Medium 2 (Reflecting Side)
Source Characteristics
Hz
Refraction & Reflection Formulas:
Z = ρ · c (Acoustic Impedance)
r_p = (Z₂ - Z₁) / (Z₂ + Z₁) (Pressure Reflection)
R = r_p² (Intensity Reflection) T_i = 1 - R (Transmission)
TL = -10 log₁₀(T_i) (dB Loss)

Calculated Wave Properties

Medium 1 Acoustic Constants
Speed of Sound (c₁) 343.2 m/s
Density (ρ₁) 1.20 kg/m³
Acoustic Impedance (Z₁) 413.2 Rayl
Wavelength (λ₁) 0.343 m
Medium 2 Acoustic Constants
Speed of Sound (c₂) 1497 m/s
Density (ρ₂) 1000 kg/m³
Acoustic Impedance (Z₂) 1.50e6 Rayl
Wavelength (λ₂) 1.497 m
Boundary Interface Coefficients
Reflection (r_p) +0.999
Transmission (t_p) 1.999
Reflected Energy (R) 99.89 %
Transmitted Energy (T) 0.11 %
Boundary Transmission Loss (TL) 29.6 dB

Doppler Shift Parameters

Physical Constants
Hz
m/s
Source Motion
m/s
Observer Motion
m/s
Doppler Equation:
f' = f · (c ± v_o) / (c ∓ v_s)
Observer approaching: +v_o, receding: -v_o
Source approaching: -v_s, receding: +v_s

Doppler Shift Results

WARNING: Source speed meets or exceeds the speed of sound! Mach >= 1. Sonic Shockwave generated.
Original Freq 1000 Hz
Observed Freq 1045 Hz
Frequency Shift +45 Hz
Pitch Change +76 cents
Source Mach Number 0.087 M
Observer Mach Number 0.044 M
Frequency vs Source Velocity

Interactive Boundary Wave Visualizer

Visualizes the sound wave traveling from Medium 1 (left) hitting the boundary interface (middle line) and propagating into Medium 2 (right). Adjust the selectors in the "Boundary Reflections" tab to see changes in Reflection Amplitude, Phase Inversion, and Transmission wavelength.

Wave Speed 1 (c₁) 343 m/s
Wave Speed 2 (c₂) 1497 m/s
Reflection Coeff (r_p) +0.999
Phase Shift (Reflected) 0° (No Inversion)