Physics 4060, Acoustics Laboratory

Because of the large range of power associated with audible sound (10¹⁴ or larger) it is customary to use the logarithmic decibel scale for sound intensity measurement. The decibel level is defined by

由于可听声与功率相关范围很大（10¹⁴或更大），因此通常使用以十为底的分贝标度来测量声强度。分贝电平定义为

where I = sound intensity = sound power per unit area (watts/cm² is a typical unit).

其中 I = 声强 = 声功率每单位面积（瓦/平方厘米是典型单位）。

此类测量的参考电平是

By examining the definition when I₀ is inserted for I, giving a 1 in the logarithm, you can see that the level I₀ is zero decibels. The threshold of pain is about 10¹³ I₀ or 130 decibels. Normal music is 40dB-100dB and conversational speech about 75dB.

通过检查当插入I₀时对I的定义，给出对数中的1，你可以看到电平I₀是零分贝。疼痛阈值约为10¹³ I₀或130分贝。正常音乐是40dB-100dB，而谈话语音约为75dB。

The just noticeable change in sound intensity is about 1 decibel. Doubling the power of a source increases the sound level by 10 log₁₀(2) = 3 decibels. This is not as dramatic a change in loudness as you might expect from power doubling - the ear's loudness response is approximately logarithmic. This might be borne in mind if you consider paying a lot more money for a 70 watt stereo rather than a 50 watt - the perceived loudness difference is slight. Subjective experiments have indicated that for a given sound the intensity must be increased by about 10 decibels to be perceived as twice as loud - a tenfold power increase!

声音强度的可察觉变化约为1分贝。使声源的功率加倍，会使声级提高10 log 10 (2) = 3分贝。这并不是你可能预期的由功率加倍带来的那么显著的响度变化——耳朵的响度响应大致是对数的。如果你考虑为70瓦立体声支付更多钱而不是50瓦的，那么感知到的响度差异很小。主观实验表明，对于同一声音，要使其被感知为两倍响度，强度必须增加约10分贝——即功率提高十倍！

In an open area with no reverberation, the sound intensity from a point source will drop off according to the inverse square law:

在无混响的开放区域中，点声源的声强将根据反平方定律衰减：

If the distance from the sound source is doubled, the intensity is down to one fourth, so

如果声源的距离加倍，强度会降至原来的四分之一，所以

A doubling of distance from the source should give you a 6 dB drop if the inverse square law holds. (Note that decibels can be used to express any sound ratio in addition to the use for comparing to hearing threshold.) If the sound intensity in an auditorium followed the inverse square law, there would be a 20 decibel drop from the nearest listener to the most distant one if the nearest were at 10 ft and the most distant at 100 ft:

如果距离声源的距离加倍，且逆平方定律成立，则应产生6 dB的衰减。（注意，分贝可以用来表示任何声音比值，而不仅仅是与听阈比较。）如果礼堂中的声音强度遵循逆平方定律，那么当最近的听众位于10英尺，最远的听众位于100英尺时，从最近的听众到最远的听众，声音强度将下降20分贝：

In any real environment - at least in any enclosed room - reverberant sound and background sound are always present and the inverse square law does not apply. If the intensity of the sound source is much greater than the background, then the sound near the source may approximate inverse square drop off- this region is often called the "direct sound field". At larger distances from the source in an acoustically "live" environment, the sound level may have little variation with distance because the room may be filled with the "reverberent sound field".

在任何真实的环境中——至少在任何封闭房间中——混响声和背景噪声总是存在的，反平方定律并不适用。如果声源的强度远大于背景噪声，那么靠近声源的声场可能近似符合反平方衰减——这一区域通常被称为‘直达声场’。在声学上‘活’的环境中，远离声源的较大距离处，声压级可能随着距离变化很小，因为房间可能充满了‘混响声场’。

II. 轮廓滤波器的使用

Sound intensity and sound "loudness" are not the same - there is not a one-to-one correlation. Two sounds of the same intensity will not in general be perceived by the human ear to have the same loudness unless the two sounds are the same pitch and of identical frequency content. The origin of this difficulty is the fact that the ear's sensitivity is strongly frequency dependent, as indicated by example contours from the human hearing curves sketched below.

声音的强度和声音的响度并不相同——它们之间没有一一对应的关系。两个强度相同的声波一般不会被人类耳朵感知为具有相同的响度，除非这两个声波的音调相同且频率成分完全一致。这种困难的根源在于人耳的灵敏度强烈依赖于频率，如下面所示意的人类听觉曲线所示。

Sounds below 100 Hz frequency are strongly discriminated against by the human ear, yet are very important for musical sound. If there is a lot of low frequency content in a sound, then a straight decibel measurement will be quite misleading if you are trying to assess loudness. A 50 dB, 1000 Hz sound will be significantly louder than a 50 dB, 100 Hz sound -- the 100 Hz sound will be barely audible. The relative loudness perception of different frequency sounds is further complicated by the fact that the response curves of the ear change with loudness level. Note that the equal loudness curve for 100 phons in the diagram above is considerably flatter that the curve for 40 phons. The human ear discriminates more and more against very low and very high frequencies as the sound gets softer. The "phon" is a unit of loudness so that a 40 phon curve is an equal-loudness curve for sounds which sound the same loudness as a 40 dB, 1000 Hz tone.

频率低于100赫兹的声音在人耳中被强烈地辨别出来，但对音乐声音却非常重要。如果一个声音中包含大量低频成分，那么当你试图评估响度时，直接使用分贝测量将非常误导。一个50分贝、1000赫兹的声音会比一个50分贝、100赫兹的声音明显更响——后者几乎听不到。不同频率声音的相对响度感知进一步复杂化的是，人耳的响应曲线会随着响度电平而变化。请注意图中100 Phon的等响曲线明显比40 Phon的曲线更平坦。人耳对非常低频和非常高频的辨别能力随着声音变弱而越来越差。“Phon”是一个响度单位，因此40 Phon曲线表示那些听起来与40分贝、1000赫兹音一样响的声音的等响曲线。

Since the human hearing response is non-uniform, standard contour filters have been developed which approximate the human hearing response. The three international standard contours are denoted A,B,C and measurements using them are denoted dBA, dBB, and dBC. These filter contours are roughly sketched below to illustrate their relative discrimination against very low and high audible frequencies.

由于人类的听觉响应是非均匀的，已开发出标准轮廓滤波器，以近似人类的听觉响应。三个国际标准轮廓分别用A、B、C表示，使用它们进行测量时分别称为dBA、dBB和dBC。这些滤波器轮廓大致如下所示，以说明它们对极低和极高可听频率的相对分辨能力。

The A contour is the most commonly used contour for the measurement of musical sound loudness, since it most accurately approximates the human hearing response for sounds of medium loudness. Note from the equal loudness curves that the hearing curve is flatter at very high sound intensity levels, so that contours B and C might be more appropriate for monitoring loud sounds. C is sometimes used for traffic noise surveys. For most purposes a survey of flat dB and dBA measurements constitutes a practical assessment of the sound field.

A轮廓是用于测量音乐声音响度最常用的轮廓，因为它最准确地近似了中等响度声音的人类听觉响应。从等响度曲线可以看出，在非常高的声强水平下，听觉曲线更平缓，因此B和C轮廓可能更适合用于监测大声响。C轮廓有时用于交通噪声调查。对于大多数用途，对平坦的dB和dBA测量进行调查，可以视为对声场的实用评估。

Physics 4060: Acoustics Laboratory

Physics 4060 Laboratory