Enter the wave speed (for electromagnetic waves in vacuum/air you can use the speed of light), the cavity length, width, height, and the mode numbers (m, n, p) into the calculator to determine the resonant frequency of that mode. This calculator can also solve for the wave speed or a missing dimension when the other values and mode numbers are known.
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Cavity Resonance Formula
The following formula is used to calculate the resonant frequency of a rectangular cavity for a specified mode (m, n, p).
f_{mnp} = \frac{v}{2}\sqrt{\left(\frac{m}{L}\right)^2+\left(\frac{n}{W}\right)^2+\left(\frac{p}{H}\right)^2}Variables:
- fmnp is the resonant frequency of mode (m, n, p) (Hz)
- v is the wave speed in the cavity medium (m/s). For electromagnetic waves in vacuum, v = c ≈ 299,792,458 m/s; in a dielectric, v is lower.
- L is the length of the cavity (m)
- W is the width of the cavity (m)
- H is the height of the cavity (m)
- m, n, p are dimensionless mode numbers (integers). They cannot all be zero.
To calculate the resonant frequency, compute (m/L)2, (n/W)2, and (p/H)2, sum them, take the square root, then multiply by v/2. A real cavity supports many resonant modes (a spectrum), so the resonant frequency depends on which (m, n, p) mode you choose.
What is a Cavity Resonance?
Cavity resonance refers to the phenomenon where waves, such as sound or electromagnetic waves, resonate or build up in intensity within a specific physical space or cavity due to constructive interference. This occurs when the cavity dimensions support standing-wave patterns (modes), causing waves to reflect back and forth and reinforce themselves at discrete resonant frequencies. This principle is used in various applications, such as in musical instruments, microwave ovens, and lasers.
