室内声学与混响时间

概述

混响时间 (RT60) 是声源在封闭空间内停止后声压级衰减 60 dB 所需的时间。它是房间声学中最重要的指标，影响语言清晰度、音乐清晰度和噪音舒适度。适当的 RT60 取决于房间体积、表面材料和预期用途。

关键公式

赛宾混响时间

$T_{60} = \frac{0.161 \, V}{A}$

将混响时间与房间体积和总吸声量关联的基础方程。

当平均吸声系数不大于约 0.35 时，赛宾公式对普通房间给出良好结果。对于平均吸声系数大于 0.35 的房间，首选艾林方程，因为对数形式能更好地表示强吸声空间。

艾林混响时间

$T_{60} = \frac{0.161 \, V}{-S \, \ln(1 - \bar{\alpha})}$

对于具有高吸声表面、平均吸声系数接近 1 的房间更准确。

总吸声量

$A = \sum_{i} \alpha_i \, S_i$

总吸声赛宾等于每个表面积乘以其在关注频率下的吸声系数之和。

房间轴向模式频率

$f = \frac{c}{2} \sqrt{\left(\frac{n_x}{L_x}\right)^2 + \left(\frac{n_y}{L_y}\right)^2 + \left(\frac{n_z}{L_z}\right)^2}$

矩形房间内的共振驻波频率，其中 $n_x, n_y, n_z$ 为非负整数。

变量

Absorption Coefficients by Material

Recommended Reverberation Times

Calculators

Sabine Reverberation Time

Absorption from Materials

单位换算器

RT60 vs Total Absorption

Design Notes

• Frequency dependence. Absorption coefficients vary significantly with frequency. Always evaluate RT60 across the 125 Hz – 4 kHz octave bands, not just at a single frequency.
• Sabine vs Eyring. Use Sabine for typical rooms with $\bar{\alpha} < 0.3$. Switch to Eyring for heavily treated rooms, anechoic spaces, or when $\bar{\alpha}$ exceeds roughly 0.3, as Sabine overestimates absorption at high coefficients.
• Audience and furniture. Unoccupied RT60 can be 20–40 % longer than occupied. Design for the occupied condition and verify that the empty condition remains tolerable.
• Air absorption. At frequencies above 2 kHz and in very large volumes (auditoria, sports halls), molecular air absorption becomes a meaningful additional decay mechanism and is not captured by the Sabine formula.
• Flutter echoes and focusing. Large parallel reflective surfaces or concave walls can produce discrete echoes and focusing even when RT60 is nominally correct. Geometry matters alongside material treatment.
• Room modes. In small rooms (studios, control rooms), low-frequency modes create pronounced peaks and nulls. Mode spacing should be analyzed; widely spaced modes below 300 Hz cause audible coloration.

还原的原始源表

以下表格还原自原始来源页面，以保留完整的参考数据。

Sound - Reverberation Time

参考资料

• Original Source – Engineering ToolBox: Room Acoustics and Reverberation