Room Acoustic Axial Standing Wave Modes
Predicts room resonance modes (axial, tangential, and oblique standing waves) where room dimensions cause bass frequency buildup and phase cancellation.
\[ f_{p,q,r} = \frac{c}{2} \sqrt{ \left(\frac{p}{L}\right)^2 + \left(\frac{q}{W}\right)^2 + \left(\frac{r}{H}\right)^2 } \]
Plain Text Formula:
f = (c / 2) * sqrt((p/L)^2 + (q/W)^2 + (r/H)^2)
📐 Variable Definitions & Parameters
| Symbol | Variable Name | Standard Unit | Physical Definition |
|---|---|---|---|
| \[ f_{p,q,r} \] | Eigenmode Frequency | Hertz (Hz) | Standing wave modal resonance frequency |
| \[ c \] | Speed of Sound | 343 m/s | Velocity of sound in air |
| \[ L, W, H \] | Room Dimensions | meters (m) | Length, width, and ceiling height of rectangular room |
| \[ p, q, r \] | Modal Integers | 0, 1, 2, 3... | Harmonic mode index along each spatial axis |
💡 Worked Engineering Example
Problem Statement:
Find the primary axial length standing wave mode (p=1, q=0, r=0) in a room 6.0 meters long.
Step-by-Step Solution:
- f = (c / 2) * (1 / L) = (343 / 2) * (1 / 6.0)
- f = 171.5 / 6.0 = 28.58 Hz
🎯 Result: The room exhibits a strong fundamental axial bass resonance at 28.58 Hz.