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Tangential Mode

A tangential mode is a room resonance involving reflections between four surfaces (two pairs of parallel walls). Tangential modes are approximately 3 dB weaker than axial modes because the sound energy is distributed across two dimensions rather than one. They are identified by mode indices where exactly one of the three indices (n₁, n₂, n₃) is zero. For example, the (1,1,0) mode involves the floor/ceiling and one pair of walls. Tangential modes fill in the frequency gaps between axial modes and contribute to the overall modal density. While individually weaker than axial modes, there are more of them, and they become increasingly important as the frequency increases toward the Schroeder frequency. In studio design, tangential modes are considered when optimizing room dimension ratios.

Formula

f = (c/2)√[(n₁/L)² + (n₂/W)²] (for n₃=0)

Unit

Expressed in Hz

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