Cavity Resonance Calculator

Cavity Resonance Formula:

\[ f = \frac{c}{2} \times \sqrt{\left(\frac{m}{a}\right)^2 + \left(\frac{n}{b}\right)^2 + \left(\frac{p}{d}\right)^2} \]

Speed of Light (c):

m/s

Mode m:

Mode n:

Mode p:

Dimension a:

Dimension b:

Dimension d:

Resonant Frequency (f):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Cavity Resonance?

Cavity resonance refers to the phenomenon where electromagnetic waves resonate within a conductive enclosure. The resonant frequencies depend on the cavity dimensions and the specific mode of oscillation defined by integer values m, n, and p.

2. How Does the Calculator Work?

The calculator uses the cavity resonance formula:

\[ f = \frac{c}{2} \times \sqrt{\left(\frac{m}{a}\right)^2 + \left(\frac{n}{b}\right)^2 + \left(\frac{p}{d}\right)^2} \]

Where:

\( f \) — Resonant frequency (Hz)
\( c \) — Speed of light (m/s)
\( m, n, p \) — Mode numbers (integers)
\( a, b, d \) — Cavity dimensions (m)

Explanation: The formula calculates the resonant frequencies of a rectangular cavity based on its physical dimensions and the specific mode of oscillation.

3. Applications of Cavity Resonance

Details: Cavity resonators are used in microwave engineering, particle accelerators, laser technology, and RF filters. They provide precise frequency control and high Q-factor in various electronic systems.

4. Using the Calculator

Tips: Enter the speed of light (typically 299792458 m/s), mode integers (m, n, p), and cavity dimensions (a, b, d) in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What are typical mode numbers?
A: Mode numbers are positive integers (0,1,2,...) but not all can be zero simultaneously. The fundamental mode typically has the lowest integers that satisfy the boundary conditions.

Q2: How does cavity shape affect resonance?
A: Different cavity shapes (cylindrical, spherical) have different resonance formulas. This calculator is specifically for rectangular cavities.

Q3: What is the significance of the speed of light in the formula?
A: The speed of light determines how quickly electromagnetic waves propagate through the cavity, directly influencing the resonant frequencies.

Q4: Can this calculator be used for acoustic cavities?
A: No, this formula is specifically for electromagnetic cavities. Acoustic cavities use different equations based on sound velocity.

Q5: What are practical considerations for real cavities?
A: Real cavities have finite conductivity, surface imperfections, and coupling elements that may slightly shift the theoretical resonant frequencies.