Document 3ejMpZ47bBm1an058j1GmYakO

-\\3- 992 CHAPTER 40 1947 Guide r quency is twice the lower frequency of the band as shown in the following table. Band Number Usual Frequency Limits Approximate Geometric Mean Frequency i 20 to 75 cps* 40 2 75 to 150 105 3 150 to 300 210 4 300 to 600 425 5 600 to 1200 850 6 1200 to 2400 1700 7 2400 to 4800 3400 8 4800 to 10,0WI* 6900 * The h ighest and lowest bands as usually used, contain somewhat more than one octave as indicated. Decibel db is a dimensionless unit for expressing the ratio of two numerical values (usually electrical or mechanical power) on a logarithmic scale. The number of decibels is ten times the logarithm to the base 10 of the numerical ratio of the two quantities. For example, let Wi and W2 desig nate two powers; or, h and I2 designate two sound intensities, and let M designate the number of corresponding decibels, then M = 10 logio El decibels Wt 0) or, M = 10 logio - decibels It (2) Alternatively, the ratio of two sound pressures squared is expressed in the same units, M = 10 logio -- = 20 logio -- decibels pi1 Pt @) These relations tacitly assume that: W = p2/Z, which means that Z, the acoustic impedance is real, and that for p\ and p2, Z\ = Z2. This is not usually the case, but because sound pressure is the easiest variable to measure in a sound field, the relation: M = 20 logio -- decibels W) is commonly used. Thus, in a sense when used in this way, the decibel is / redefined on the basis of a pressure squared ratio rather than a power ratio. Sound Power Level PWL is ten times the logarithm to the base ten of the ratio of the sound power to the reference power of 10"13 watt. Thus, Power Level in the English system:2 PWL = 10 logio dbe 10 18 <5) where W = sound power, watts. The unit is the dbe. The symbol dbe means that the sound power level Sound Control 993 is convenient to use in the English system and that 10"13 watt is the refer ence power. Sound Intensity Level (Lj) is ten times the logarithm to the base ten of the ratio of the sound intensity I to the reference intensity of 10"16 watt per sq cm (or its equivalent 1 picowatt per sq m). Thus la = 10 logio dbi (6) where or I = watts per square centimeter. la = 10 logio dbi 10-" (7) where l = watts per square meter. The unit is the dbi. Either formula gives the same numerical result. Sound Pressure Level Lp is twenty times the logarithm to the base 10 of the ratio of the sound pressure p to the reference sound pressure of 0.0002 microbar, i.e., where Lp = 20 logio P dbe 0.0002 (8) p = sound pressure, microbars (dynes per square centimeter). The unit is the dbe, where c stands for the C scale or flat scale on the sound level meter. Loudness N is the intensive subjective attribute of an auditory sensation, m terms of which sounds may be ordered on a scale extending from soft to loud. The unit is the sone. The number of sones is directly proportional to the loudness. By definition, a 1000 cps pure tone with a sound pressure level of 40 dbe has a loudness of 1.0 sone. Loudness Level (L*,) of a sound is numerically equal to the sound pres sure level Lp of a simple tone of frequency 1000 cps that is judged by the listeners to be equivalent in loudness. The unit is the phon. In this text, for a 1000 cps tone, Lk in phons is assumed to be related to AT in sones by the formula Ln = 33 logio IV + 40 phons (9) This approximation is assumed valid3 for N > 1. Sound Level at a point in a sound field is the reading in decibels of a sound f a meJ,er constructed and operated in accordance with the latest edition of American Standard Sound Level Meters for the Measurement of Noise and Other Sounds.4 The reading is taken with the proper weighting net work switched into the circuit. The unit is dba, if the reading is taken on the A scale; dbb if taken on the B scale, and dbe if taken on the C or flat scale. The use of these scales is discussed later. Attenuation is ten times the logarithm to the base ten of the ratio of the l?uhd intensities at any two points along any continuous acoustic path in he direction away from the source. The unit is the decibel. For a signal