Calculator Inputs
The page stays single-column overall, while the input grid becomes three columns on large screens, two on tablets, and one on mobile.
Example Data Table
These sample cases illustrate normal-incidence transmission behavior across different impedance mismatches.
| Case | Mode | Z1 | Z2 | r | t | T Power |
|---|---|---|---|---|---|---|
| Case 1 | Generic | 400 | 800 | -0.3333 | 0.6667 | 88.8889% |
| Case 2 | Generic | 750 | 750 | 0.0000 | 1.0000 | 100.0000% |
| Case 3 | String | 1.5492 | 3.0984 | -0.3333 | 0.6667 | 88.8889% |
Formula Used
Characteristic impedance
Generic mode: Use the entered values directly.
Acoustic mode: Z = ρc
String mode: Z = √(Tμ)
Lossless normal-incidence coefficients
Reflection amplitude coefficient: r = (Z1 - Z2) / (Z1 + Z2)
Transmission amplitude coefficient: t = 2Z1 / (Z1 + Z2)
Reflection power coefficient: R = r²
Transmission power coefficient: T = 4Z1Z2 / (Z1 + Z2)²
Derived outputs
Reflected amplitude = Ai × r
Transmitted amplitude = Ai × t
Mismatch loss = -10 log10(T)
Return loss = -20 log10(|r|)
These equations assume a linear, lossless interface at normal incidence. Oblique incidence, anisotropy, dispersion, and strongly lossy media need extended models.
How to Use This Calculator
- Select a calculation mode that matches your physics problem.
- Enter the incident amplitude and frequency.
- Provide either direct impedances, acoustic properties, or string properties.
- Choose a sweep range to visualize how mismatch changes transmission.
- Press Calculate Transmission to show results above the form.
- Review coefficients, amplitudes, losses, wavelengths, and the Plotly graph.
- Use the CSV button for spreadsheet work and the PDF button for reports.
Frequently Asked Questions
1) What does the transmission coefficient represent?
It measures how much of an incident wave crosses a boundary into the second medium. This calculator reports both amplitude transmission and transmitted power for a lossless normal-incidence interface.
2) Why do impedance values matter so much?
Impedance controls how strongly a boundary resists wave motion. When impedances match, reflection vanishes and transmission reaches its maximum possible value for the modeled interface.
3) What is the difference between amplitude and power transmission?
Amplitude transmission tracks the wave variable itself, while power transmission tracks transferred energy. They are related, but they are not numerically identical when impedances differ.
4) When should I use acoustic mode?
Use acoustic mode when you know density and wave speed for each medium, such as air, water, gels, or solids under a simplified normal-incidence sound model.
5) When should I use string mode?
Use string mode for transverse waves crossing a junction between two stretched strings. The calculator derives impedance from tension and linear mass density automatically.
6) Why is the reflection coefficient sometimes negative?
A negative reflection coefficient indicates phase inversion of the reflected wave relative to the incident wave. The sign affects amplitude direction, while reflected power remains positive.
7) Does this tool cover oblique incidence or multilayer stacks?
No. This version is designed for a single interface at normal incidence. Multilayer interference, angle-dependent refraction, and lossy propagation require broader transfer-matrix models.
8) What do mismatch loss and return loss tell me?
Mismatch loss shows energy lost from imperfect transfer. Return loss shows how much signal is reflected back. Higher return loss generally indicates a better impedance match.