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Room Mode Frequency Calculation

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To visualize the mode of a specific resonance frequency in a room, click on the little square 🧊. A new tab will open with a 3D view.

Acoustic Room Mode Calculation

The acoustic room mode refers to the natural resonant frequencies of a room, which occur due to standing waves between the room's surfaces. These modes can significantly affect the acoustic quality of the room, leading to either amplification or attenuation of certain frequencies.

Room Mode Calculation Formula

The resonant frequencies, or room modes, are calculated using the following formula:

\[ f_{n_x,n_y,n_z} = c_0 \left[ \frac{1}{2} \left( \left( \frac{n_x}{L_x} \right)^2 + \left( \frac{n_y}{L_y} \right)^2 + \left( \frac{n_z}{L_z} \right)^2 \right)^{\frac{1}{2}} \right] \]

Where:

  • \( f_{n_x,n_y,n_z} \): The frequency of the room mode in Hz.
  • \( c_0 \): The speed of sound in air, approximately 343 m/s at room temperature.
  • \( n_x, n_y, n_z \): Mode numbers for the dimensions along the x, y, and z axes, representing the harmonic order in each direction.
  • \( L_x, L_y, L_z \): The dimensions of the room along the x, y, and z axes, respectively.

Visualization of the Room Modes


The calculation done to visualize the room modes in the assumption of rigid walls and rectangular room is given below [1]

\[ p = \bar{p} \cos\left( \frac{\pi n_x x}{L_x} \right) \cos\left( \frac{\pi n_y y}{L_y} \right) \cos\left( \frac{\pi n_z z}{L_z} \right) e^{j \omega t} \]

Understanding Room Modes


Room modes typically occur at frequencies where the wavelength of the sound is equal to or a multiple of the room's dimensions. These modes are important to consider in acoustic design, as they can create areas of high and low pressure, which may cause unwanted resonances or dead spots in the room.

Three types of room modes are typically considered:

  • Axial modes: These occur between two parallel surfaces, such as opposite walls or the floor and ceiling.
  • Tangential modes: These involve four room surfaces, typically two pairs of opposite walls.
  • Oblique modes: These involve all six surfaces of the room (four walls, ceiling, and floor).

How to Measure Standing Waves in a Room

Measuring standing waves in a room involves exciting the space with low-frequency sound, typically using a subwoofer or a swept sine tone. A measurement microphone is placed at various locations and connected to an acoustic analysis tool to capture the room’s frequency response.

To identify these resonances, the recorded signals are analyzed using a real-time analyzer (RTA) or through Fast Fourier Transform (FFT) techniques. By moving the microphone around the room, you can observe changes in sound pressure, helping to locate nodes (low-pressure areas) and antinodes (high-pressure areas).

Room modes are particularly noticeable in small or rectangular rooms, where certain frequencies are amplified. Understanding and calculating these modes is essential for optimizing room acoustics, especially in recording studios, home theaters, and other sound-sensitive environments.


[1] - Engineering Noise Control Theory and Practice-Bies


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