Q: How is Speaker Boundary Interference Response (SBIR) first quarter-wave cancellation calculated?

When a loudspeaker is placed at distance d from a rigid boundary, the reflected wave travels an extra distance of 2d. Destructive interference (180-degree phase cancellation) occurs when 2d equals half a wavelength, yielding the primary notch frequency f_null = c / (4 * d).

Question 1

How are room standing wave (room mode) frequencies calculated?

Accepted Answer

Room eigenfrequencies in a rectangular enclosure are calculated using the Rayleigh 3D wave equation: f(nx, ny, nz) = (c / 2) * sqrt((nx/L)^2 + (ny/W)^2 + (nz/H)^2), where c ≈ 343 m/s is the speed of sound, L, W, H are room dimensions in meters, and nx, ny, nz are non-negative integers representing axial, tangential, and oblique modes.

Question 2

What is the difference between Sabine and Eyring RT60 reverberation formulas?

Accepted Answer

Sabine's equation (RT60 = 0.161 * V / A) assumes a diffuse sound field with low average absorption (alpha < 0.25). Eyring's equation (RT60 = 0.161 * V / [-S * ln(1 - alpha_bar) + 4mV]) accounts for discrete energy loss per reflection and is essential for acoustically treated studios, home theaters, and control rooms where average absorption exceeds 0.25.

Question 3

How is Speaker Boundary Interference Response (SBIR) first quarter-wave cancellation calculated?

Accepted Answer

When a loudspeaker is placed at distance d from a rigid boundary, the reflected wave travels an extra distance of 2d. Destructive interference (180-degree phase cancellation) occurs when 2d equals half a wavelength, yielding the primary notch frequency f_null = c / (4 * d).

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