Calculate rectangular cavity resonance frequency or solve for wave speed, length, width, or height from mode numbers m, n, and p in any unit.
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Cavity Resonance Formula
The calculator uses the rectangular cavity resonance relationship for a mode identified by three nonnegative integer mode numbers: m, n, and p.
To solve for wave speed:
To solve for cavity length:
To solve for cavity width:
To solve for cavity height:
- fmnp = resonance frequency for the selected cavity mode
- v = wave speed in the cavity medium
- L = cavity length
- W = cavity width
- H = cavity height
- m = length-direction mode number
- n = width-direction mode number
- p = height-direction mode number
The calculator can find the missing value when you enter the mode numbers and exactly four of these five values: frequency, wave speed, length, width, and height. It first converts the selected units to base units, applies the formula, then converts the result back to the unit you selected.
If you solve for a dimension, the corresponding mode number must be greater than zero. For example, you cannot solve for L when m = 0, because that mode does not depend on the length term.
Common Wave Speeds for Cavity Calculations
Use a wave speed that matches the type of wave and the medium inside the cavity.
| Wave or medium | Typical speed | Use case |
|---|---|---|
| Sound in air at about 20°C | 343 m/s | Acoustic cavity or room mode estimates |
| Sound in water | about 1480 m/s | Fluid-filled acoustic cavities |
| Electromagnetic wave in vacuum or air | 299,792,458 m/s | Microwave or RF rectangular cavities |
| Electromagnetic wave in a dielectric | c / sqrt(εrμr) | Cavities filled with non-air material |
Mode Number Reference
| Mode numbers | What changes the frequency? | Notes |
|---|---|---|
| (1, 0, 0) | Length only | Frequency is independent of width and height. |
| (0, 1, 0) | Width only | Frequency is independent of length and height. |
| (0, 0, 1) | Height only | Frequency is independent of length and width. |
| (1, 1, 1) | Length, width, and height | All three dimensions contribute to the resonance. |
Example Calculations
Example 1: Calculate resonance frequency
Suppose the wave speed is 343 m/s, the cavity dimensions are L = 0.5 m, W = 0.4 m, H = 0.3 m, and the mode is (1, 1, 1).
The resonance frequency is about 792.8 Hz.
Example 2: Calculate cavity length
Suppose the resonance frequency is 500 MHz, the wave speed is 299,792,458 m/s, and the mode is (1, 0, 0). Since only the length term is active, the width and height do not affect this mode.
The required cavity length is about 0.2998 m, or about 30.0 cm.
FAQ
Why can the mode numbers not all be zero?
If m, n, and p are all zero, every term inside the square root becomes zero. That would give a zero-frequency result, which is not a usable cavity resonance mode in this formula. At least one mode number must be greater than zero.
What happens if one mode number is zero?
A zero mode number removes that direction from the frequency calculation. For example, if m = 0, the term (m/L)2 is zero, so the resonance frequency does not depend on length. That is why you cannot solve for length when m = 0.
Why do I need to enter exactly four of the five main values?
The formula has five main physical values: frequency, wave speed, length, width, and height. The calculator needs four known values to solve for the one missing value. If you enter fewer than four, there is not enough information. If you enter all five, there is no missing value to calculate.
