Physics 4060, Acoustics Laboratory

The most important single parameter for the evaluation of auditorium acoustics is the reverberation time . Reverberation may be defined as the sum of the reflected sound energy from the surfaces of the enclosure. Hence in a perfect anechoic chamber there would be no reverberation at all since all sound energy is absorbed at its first interaction with the walls. An isolated point source, remote from any surfaces would produce no reverberation since there is no reflection; the inverse-square law applies. An auditorium produces a departure from the inverse-square law because the reflected sound adds to the direct sound at a given location. A certain amount of reverberation is highly desirable since it adds richness to the sound and prevents the loudness of the sound from dropping off so steeply as you move toward the back of the auditorium. However, excessive reverberation "muddies" the sound and makes speech garbled and unintelligible. Hence the need for a measurable parameter with which to evaluate the amount of reverberation: the reverberation time.

对声学评价最重要的单一参数是混响时间。混响可以定义为从房间表面反射的声能之和。因此，在一个完全消声的房间中，完全没有混响，因为所有声能在第一次与墙壁相互作用时都会被吸收。一个远离任何表面的孤立点声源不会产生混响，因为没有反射；平方反比定律适用。而一个礼堂由于反射声在某一位置与直达声叠加，会偏离平方反比定律。一定量的混响是高度可取的，因为它能增加声音的丰富性，并防止当你向礼堂后部移动时声音的响度迅速下降。然而，过多的混响会使声音变得模糊，并使言语变得含糊不清。因此，需要一个可测量的参数来评估混响的量：混响时间。

If you clap your hands in an empty auditorium, you hear the sound die away until it is no longer audible above the background sound level in the enclosure. In another auditorium which is more "live" you note that the sound takes longer to die away, while one in which the sound fades too quickly is said to be "dead". This experience gets at the basic idea of the reverberation time, but a precise quantitative definition is desirable since the time to die away to background depends on the loudness of the original sound and the background level. The stantard definition of reverberation time is the time required to drop 60 decibels below the original sound level. This is an arbitrary definition, but has some rationale in the fact that orchestral music is usually in the range 40 to 100 decibels and a typical auditorium background is about 40 decibels. Hence this definition of reverberation time is about the time required for the highest crescendo of the orchestra to die away to room background level. The desirable range of reverberation times for general purpose auditoriums is about 1.5 to 2.5 seconds. Longer reverberation times are sometimes desirable for music and somewhat shorter reverberation times are better if the auditorium is to be used for speech only.

如果你在空荡的礼堂中拍手，你会听到声音逐渐消失，直到它在封闭空间中不再高于背景噪声水平。在另一个更‘活’的礼堂中，你会注意到声音消失得更慢，而一个声音迅速衰减的礼堂则被称为‘死’。这种体验触及了混响时间的基本概念，但由于声音消失到背景噪声水平的时间取决于原始声音的响度和背景噪声水平，因此需要一个精确的定量定义。混响时间的标准定义是声音需要下降60分贝到原始声音水平所需的时间。这是一个任意的定义，但有其理由，因为交响乐通常在40到100分贝之间，而典型礼堂的背景噪声大约为40分贝。因此，这种混响时间的定义大约是交响乐最高高潮部分消失到房间背景噪声水平所需的时间。一般用途礼堂的混响时间理想范围约为1.5到2.5秒。对于音乐，较长的混响时间有时是可取的，而如果礼堂仅用于演讲，则略短的混响时间会更好。

The reverberation time can be measured by producing white noise in the enclosure at a level 60 dB above background, switching it off, and measuring the time it takes to drop back to background. The drawbacks to this method are that it takes a high power source and the noise produced is unpleasantly loud. Measuring the time required for a smaller intensity drop and extrapolating to the 60 dB time is the usual procedure. This requires some calculation and a mathematical model for the decay curve of the sound in the enclosure.

混响时间可以通过在密闭空间内产生比背景噪声高60 dB的白噪声，然后关闭该噪声并测量其衰减到背景水平所需的时间来测量。这种方法的缺点是需要高功率的电源，且产生的噪声听起来很刺耳。通常的做法是测量较小的声压级下降所需时间，并将其外推到60 dB的混响时间。这需要一些计算和对密闭空间内声音衰减曲线的数学模型。

If a sound source of intensity I₀ is switched off at time t=0, then the sound starts to die away and will be 60 dB down (or 10^-6 I₀) at a time t=T, one reverberation time later. If the sound field decay can be modeled by an exponential curve then

如果在时间t=0时关闭一个强度为I₀的声源，那么声音开始衰减，经过一个混响时间T后，声音强度将下降60 dB（或10⁻⁶I₀）。如果声场衰减可以被建模为指数曲线，则

where T is the reverberation time (sometimes called RT₆₀ as a mnemonic for its definition). To evaluate the scaling constant a , note that

其中 T 是混响时间（有时也称为 RT 60，作为其定义的缩写）。为了评估比例常数 a，注意以下内容。

对两边取自然对数得到

This evaluation will permit a calculation of the reverberation time T if any two intensities I₀ and I are measured along with the time interval t between the two measurements. From equation (2) the relationship for T is

这种评估将允许计算混响时间T，如果在两个测量之间测量了两个强度I₀和I，并且知道这两个测量之间的时间间隔t。根据方程(2)，T的关系为

If a storage oscilloscope is adjusted for a slow sweep, the decay of the sound field will appear something like Figure 1. However, the voltage from the microphone is being displayed rather than intensity, and the intensity is proportional to the square of the voltage. In terms of the measured voltages, the reverberation time relationship from (3) becomes

如果存储示波器调整为慢速扫描，声音场的衰减将看起来像图1所示。然而，显示的是麦克风的电压而非强度，而强度与电压的平方成正比。在测量的电压方面，式(3)中的混响时间关系变为

这是实验中用来确定的关系

从示波器测量电压和时间。

the reverberation time of the room. It could then be compared with the approximate relationship

房间的混响时间。它就可以与近似关系进行比较

where V = room volume in cubic meters, S = surface area in square meters, and a = average absorption coefficient. The rough absorption coefficient obtained in this manner could help to evaluate the change which might be made in the reverberation time by changing the surfaces (carpet, curtains, etc. ). Absorption coefficients for standard building materials are available in tables.

其中，V 为房间体积（立方米），S 为表面积（平方米），a 为平均吸收系数。通过这种方式获得的粗糙吸收系数可以帮助评估通过改变表面（地毯、窗帘等）所可能带来的混响时间的变化。标准建筑材料的吸收系数可在表中查到。

Connect the white noise generator to the audio amplifier so that white noise can be produced in the room. Choose a distance from the loudspeakers which could be considered to be and "ideal listener" location. Set up the sound level meter at that point and connect its output to the storage oscilloscope. Measure the background level in dB (20 kHz position) and produce white noise in the room at least 10 dB and preferrably 20-30 dB above background. Put the oscilloscope on single sweep, storage mode and set the sweep time slow enough that you can react to the sweep and switch off the sound once the trace is started. The faster the sweep, the better your time resolution, so some experimentation will be necessary.

将白噪声发生器连接到音频放大器，以便在房间内产生白噪声。选择一个距离扬声器的距离，可以被认为是‘理想听众’的位置。在该点设置声音电平计，并将其输出连接到存储示波器。测量背景电平（20 kHz位置）的分贝数，并在房间内产生至少比背景高10 dB， preferably 20-30 dB的白噪声。将示波器设置为单次扫描、存储模式，并将扫描时间调慢，以便你可以及时反应并一旦迹线开始扫描就关闭声音。扫描速度越快，时间分辨率越好，因此需要一些实验。

With about four repetitions, take the data on voltage and time during the decay as indicated in Figure 1 and calculate the reverberation time for each. Average to get a final result. Make a rough measurement of the room dimensions and calculate an average absorption coefficient.

在大约四次重复中，根据图1中所示的数据，在衰减过程中测量电压和时间，对每个数据计算混响时间。取平均值以得到最终结果。粗略测量房间的尺寸，并计算平均吸收系数。

The reverberation time discussed above is an overall average reverberation time, including all sound frequencies. The variation of reverberation time with frequency is also important. In the auditoriums and opera halls which are judged to have the best acoustics, the reverberation time for low frequencies is considerably longer than that for high frequencies. A rule of thumb is that the reverberation time for lows is about 40% longer than that for highs in these enclosures. You can observe this effect by clapping your hands sharply in a quiet auditorium. The initial sound is a sharp sound containing many high frequencies, while the last sound heard as the sound dies away is a low frequency sound.

上文讨论的混响时间是一个总体平均的混响时间，包括所有声音频率。混响时间随频率的变化也很重要。在被判定具有最佳声学性能的音乐厅和歌剧院中，低频的混响时间明显长于高频的混响时间。一个粗略的规则是，在这些空间中，低频的混响时间大约比高频的长40%。你可以通过在安静的音乐厅中突然拍手来观察这种效应。初始的声音是一个尖锐的声音，包含许多高频成分，而当声音逐渐消失时，最后听到的声音则是一个低频声音。

A longer reverberation time for low frequencies gives you an effective "bass boost" in the rear of the auditorium where the reverberant sound is a larger fraction of the total ambient sound. This need for a bass boost in the areas of the enclosure where the sound is softest is a characteristic of the human hearing response. As indicated in Figure 2, the equal loudness curve for human hearing is "flatter" at loud sound levels than it is at softer sound levels. The sensitivity of the ear to low frequencies drops off more rapidly than that for midrange frequencies as the sound intensity is decreased.

低频的混响时间更长，会在观众席后方产生有效的‘低音增强’效果，因为混响声在总环境声中占更大比例。在 enclosure 中声场最软的区域需要低音增强，这是人类听觉响应的一个特征。如图2所示，人耳的等响度曲线在大声量级时比在小声量级时更平坦。随着声强减小，人耳对低频的灵敏度下降速度比对中频的灵敏度要快。

Figure 2. The change of the human hearing response curve with changing loudness.

图2 人类听觉响应曲线随响度变化而变化。

A musical composition which is perceived to be well balanced at the front of the auditorium will be perceived to be deficient in bass at the rear of the auditorium unless some bass boost occurs. This is often explained by saying "High frequencies carry better than low frequencies." - but in terms of the sound transmission, quite the opposite is true. You have no doubt observed that the thunder from nearby lightning is a sharp crack, while distant thunder is a low rumble. Part of the physical reason is that high frequency sounds are absorbed by the air more efficiently than lows - hence more of the lows reach you over a long distance. This low rumble of distant thunder is also enhanced by the fact that low frequencies are more efficiently structure-borne through the earth, buildings, etc. Also, their longer wavelengths lead to more diffraction around buildings and other obstructions in their path. The situation in an auditorium differs in that none of the "distant thunder" effects really apply, and one can reasonably assume that all frequencies travel equally well. Air absorption is not a significant factor in most auditoriums, so the bass boost occurs because most building materials, particularly woods, absorb high frequencies more readily than low frequencies.

在观众席前部听起来平衡的音乐作品，在观众席后部会显得低音不足，除非有低音增强。这通常被解释为‘高频传播比低频更好’，但就声音传播而言，事实恰恰相反。你可能已经观察到，近处的雷声是尖锐的爆裂声，而远处的雷声则是一阵低沉的轰鸣。部分物理原因在于，高频声音比低频声音更高效地被空气吸收——因此，更多的低频声音能够传播更远的距离。远处的雷声轰鸣也受到低频声音更有效地通过地面、建筑物等结构传播的增强，以及它们更长的波长导致在路径中更容易绕过建筑物和其他障碍物。而在音乐厅中，情况则不同，不存在所谓的‘远处雷声’效应，可以合理地假设所有频率传播效果相当。在大多数音乐厅中，空气吸收不是重要因素，因此低音增强是因为大多数建筑材料，特别是木材，比低频更容易吸收高频。

In summary, if the sound is soft it needs to have more bass because the ear discriminates against low frequencies more and more as the sound gets softer. This is shown by the comparison of the human hearing curves for loud and soft sounds in Figure 3. The rise in the low frequency end of the hearing curve for soft sounds means that more low frequency sound energy will be needed to achieve equal loudness. This undesirable bass discrimination of the ear is overcome if there is more low frequency reverberation than high in the auditorium. The needed bass boost is contributed by having a longer reverberation time for low frequencies.

总之，如果声音较弱，它需要更多的低音，因为耳朵对低频的辨别能力随着声音变弱而越来越差。这在图3中通过人类听觉曲线在响度不同情况下的比较得以体现。对于弱声，听觉曲线在低频端的上升意味着要达到同等响度需要更多的低频声能。这种不希望的低音辨别能力可以通过在礼堂中低频混响多于高频来克服。所需的低音增强则通过为低频提供更长的混响时间来实现。

Pass the output of the white noise generator through the Pasco tunable filter to the audio amplifier. Use the "band pass" mode of the filter to transmit only a norrow band of frequencies. Start with 100 Hz and measure the reverberation time as described in the previous section. Repeat for 200, 400, 800, 1200, 1600, 2000, 4000 Hz and plot the reverberation time as a function of frequency.

将白噪声发生器的输出通过Pasco可调滤波器传递到音频放大器。使用滤波器的'带通'模式，仅传输一个狭窄的频率范围。从100 Hz开始，按照上一节所述方法测量混响时间。依次进行200 Hz、400 Hz、800 Hz、1200 Hz、1600 Hz、2000 Hz和4000 Hz的测量，并将混响时间作为频率的函数进行绘制。

Figure 3. A longer reverberation time for low frequencies gives a needed bass boost in the rear of an auditorium.

Reverberation Time

Physics 4060: Acoustics Laboratory

Physics 4060 Laboratory