Enter the magnetic permeability, box dimensions, mode numbers, and dielectric constant into the calculator to determine the box resonance cutoff frequency.

## Box Resonance Formula

The following equation is used to calculate the Box Resonance.

f = C / (2*sqrt(e*u)) * sqrt ( m/a^2 + n/b^2 + p/h^2)

- Where f is the cutoff frequency
- C is a constant (3×10^11 mm/s)
- e is the dielectric constant
- u is the magnetic permeability
- a,b,h are the length, width, and height respectively
- m,n,p are the mode numbers for each respective dimension

## What is a Box Resonance?

Box resonance refers to the phenomenon that occurs when sound waves produced within an enclosed space, such as a box or container, interact with the structure’s walls. This interaction leads to the amplification or attenuation of specific frequencies, resulting in certain tones being emphasized or diminished.

When sound is produced within a box, it travels in waves, bouncing off the walls and reflecting back into the box.

These reflected waves interfere with the original sound waves, either reinforcing or canceling out specific frequencies.

The dimensions, material, and construction of the box determine the resonant frequencies it will amplify or dampen.

## How to Calculate Box Resonance?

Example Problem:

The following example outlines the steps and information needed to calculate Box Resonance.

First, determine the dielectric constant and magnetic permeability. In this example, these are given as 1 and 2, respectively.

Next, determine the length, width, and height of the box. These are measured to be 3,4, and 2, respectively.

Next, determine the mode numbers at these dimensions. These are found to be 5,6, and 10, respectively.

Finally, calculate the box resonance using the formula above:

f = C / (2*sqrt(e*u)) * sqrt ( m/a^2 + n/b^2 + p/h^2)

f = (3*10^11)/ (2*sqrt(1*2)) * sqrt ( (5/3)^2 + (6/4)^2 + (10/2)^2)

f = 581216396878