## Equivalent Sound Level and Its Relationship to Other Noise Measures

 The following text is Appendix A in Information on Levels of Environmental Noise Requisite to Protect Public Health and Welfare with an Adequate Safety Margin, U.S. Environmental Protection Agency, 1974 (EPA/ONAC 550/9-74-004).

DEVELOPMENT OF EQUIVALENT SOUND LEVEL

The accumulated evidence of research on human response to sound indicates clearly that the magnitude of sound as a function of frequency and time are basic indicators of human response to sound. These factors are reviewed here, and it is concluded that it is not necessary to invent a new concept for the purpose of identifying levels of environmental noise.

Magnitude

Sound is a pressure fluctuation in the air; the magnitude of the sound describes the physical sound in the air; (loudness, on the other hand, refers to how people judge the sound when they hear it). Magnitude is stated in terms of the amplitude of the pressure fluctuation. The range of magnitude between the faintest audible sound and the loudest sound the ear can withstand is so enormous (a ratio of about 1,000,000 to I ) that it would be very awkward to express sound pressure fluctuations directly in pressure units. Instead, this range is "compressed" by expressing the sound pressure on a logarithmic scale. Thus, sound is described in terms of the sound pressure level (SPL), which is ten times the common logarithm of the ratio of the square of the sound pressure in question to the square of a (stated or understood) reference sound pressure, almost always 20 micropascals.* [*One pascal = one newton per square meter.] Or, in mathematical terms, sound pressure level L expressed in decibels is:

L = 10 log (p2/po2)
where p is the pressure fluctuation and po is the reference pressure.

Frequency Characteristics of Noise

The response of human beings to sound depends strongly on the frequency of sound. In general, people are less sensitive to sounds of low frequency, such as 100 hertz (Hz),* [*Hertz is the international standard unit of frequency, until recently called cycles per second; it refers to the number of pressure fluctuations per second in the sound wave.] than to sounds at 1000 Hz; also at high frequencies such as 8000 Hz, sensitivity decreases. Two basic approaches to compensate for this difference in response to different frequencies are (1) to segment the sound pressure spectrum into a series of contiguous frequency bands by electrical filters so as to display the distribution of sound energy over the frequency range; or (2) to apply a weighting to the overall spectrum in such a way that the sounds at various frequencies are weighted in much the same way as the human ear hears them.

In the first approach a sound is segmented into sound pressure levels in 24 different frequency bands, which may be used to calculate an estimate of the "loudness" or "noisiness" sensation which the sound may be expected to cause. This form of analysis into bands is usually employed when detailed engineering studies of noise sources are required. It is much too complicated for monitoring noise exposure.

To perform such analysis, especially for time-varying sounds, requires a very complex set of equipment. Fortunately, much of this complication can be avoided by using approach 2, i.e., by the use of a special electrical weighting network in the measurement system. This network weights the contributions of sounds of different frequency so that the response of the average human ear is simulated. Each frequency of the noise then contributes to the total reading by an amount approximately proportional to the subjective response associated with that frequency. Measurement of the overall noise with a sound level meter incorporating such a weighting network yields a single number, such as the A-weighted Sound Level, or simply A-level, in decibels. For zoning and monitoring purposes, this marks an enormous simplification. For this reason, the A-level has been adopted in large-scale surveys of city noise coming from a variety of sources. It is widely accepted as an adequate way to deal with the ear's differing sensitivity to sounds of different frequency, including assessment of noise with respect to its potential for causing hearing loss. Despite the fact that more detailed analysis is frequently required for engineering noise control, the results of such noise control are adequately described by the simple measure of sound level.

One difficulty in the use of a weighted sound level is that psychoacoustic judgment data indicate that effects of tonal components are sometimes not adequately accounted for by a simple sound level. Some current ratings attempt to correct for tonal components; for example, in the present aircraft noise certification procedures, "Noise Standards: Aircraft Type Certification," FAR Part 36, the presence of tones is identified by a complex frequency analysis procedure. If the tones protrude above the adjacent random noise spectrum, a penalty is applied beyond the direct calculation of perceived noise level alone. However, the complexities involved in accounting for tones exceed practicable limits for monitoring noise in the community or other defined areas. Consequently, EPA concludes that, where appropriate, standards for new products will address the problem of tones in such a way that manufacturers will be encouraged to minimize them and, thus, ultimately they will not be a significant factor in environmental noise.

With respect to both simplicity and adequacy for characterizing human response, a frequency-weighted sound level should be used for the evaluation of environmental noise. Several frequency weightings have been proposed for general use in the assessment of response to noise, differing primarily in the way sounds at frequencies between 1000 and 4000 Hz are evaluated. The A-weighting, standardized in current sound level meter specifications, has been widely used for transportation and community noise description. [Ref. 1] For many noises the A-weighted sound level has been found to correlate as well with human response as more complex measures, such as the calculated perceived noise level or the loudness level derived from spectral analysis. [Ref. 2] However, psychoacoustic research indicates that, at least for some noise signals, a different frequency weighting which increases the sensitivity to the 1000-4000 Hz region is more reliable. [Ref. 3] various forms of this alternative weighting function have been proposed; they will be referred to here as the type "D-weightings". None of these alternative weightings has progressed in acceptance to the point where a standard has been approved for commercially available instrumentation.

It is concluded that a frequency-weighted sound pressure level is the most reasonable choice for describing the magnitude of environmental noise. In order to use available standardized instrumentation for direct measurement, the A frequency weighting is the only suitable choice at this time.* [*All sound levels in this report are A-weighted sound pressure levels in decibels with reference to 20 micropascals.] The indication that a type D-weighting might ultimately be more suitable than the A-weighting for evaluating the integrated effects of noise on people suggests that at such time as a type D-weighting becomes standardized and available in commercial instrumentation, its value as the weighting for environmental noise should be considered to determine if a change from the A-weighting is warranted.

Time Characteristics Of Noise

The dominant characteristic of environmental noise is that it is not steady-at any particular location the noise usually fluctuates considerably, from quiet at one instant to loud the next. Thus, one cannot simply say that the noise level at a given location or that experienced by a person at that location is "so many decibels" unless a suitable method is used to average the time-varying levels. To describe the noise completely requires a statistical approach. Consequently, one should consider the noise exposure, which is received by an individual moving through different noisy spaces. This exposure is related to the whole time-varying pattern of sound levels. Such a noise exposure can be described by the cumulative distribution of sound levels, showing exactly what percent of the whole observation period each level was exceeded.

A complete description of the noise exposure would distinguish between daytime, evening and nighttime, and between weekday and weekend noise level distributions. It would also give distributions to show the difference between winter and summer, fair weather and foul.

The practical difficulty with the statistical methodology is that it yields a large number of statistical parameters for each measuring location; and even if these were averaged over more or less homogeneous neighborhoods, it still would require a large set of numbers to characterize the noise exposure in that neighborhood. It is literally impossible for any such array of numbers to be effectively used either in an enforcement context or to map existing noise exposure baselines.

It is essential, therefore, to look further for a suitable single-number measure of noise exposure. Note that the ultimate goal is to characterize with reasonable accuracy the noise exposure of whole neighborhoods (within which there may actually exist a fairly wide range of noise levels), so as to prevent extremes of noise exposure at any given time, and to detect unfavorable trends in the future noise climate. For these purposes, pinpoint accuracy and masses of data for each location are not required, and may even be a hindrance, since one could fail to see the forest for the trees.

A number of methodologies for combining the noise from both individual events and quasi-steady state sources into measures of cumulative noise exposure have been developed in this country and in other developed nations, e.g., Noise Exposure Forecast, Composite Noise Rating, Community Noise Equivalent Level, Noise and Number Index, and Noise Pollution Level. Many of these methodologies, while differing in technical detail (primarily in the unit of measure for individual noise events), are conceptually similar and correlate fairly well with each other. Further, using any one of these methodologies, the relationships between cumulative noise exposure and community annoyance [Refs.4, 5] also correlate fairly well. It is therefore unnecessary to invent a new concept for the purpose of identifying levels of environmental noise. Rather, it is possible to select a consistent measure that is based on existing scientific and practical experience and methodology and which meets the criteria presented in Section 2 of the body of this document. Accordingly, the Environmental Protection Agency has selected the Equivalent Sound Level (Leq) for the purpose of identifying levels of environmental noise.

Equivalent Sound Level is formulated in terms of the equivalent steady noise level which in a stated period of time would contain the same noise energy as the time-varying noise during the same time period.

The mathematical definition of Leq for an interval defined as occupying the period between two points in time t1 and t2 is:

where p(t) is the time varying sound pressure and po is a reference pressure taken as 20 micropascals.

The concept of Equivalent Sound Level was developed in both the United States and Germany over a period of years. Equivalent level was used in the 1957 original Air Force Planning Guide for noise from aircraft operations, [Ref. 6] as well as in the 1955 report [Ref. 7] on criteria for short-time exposure of personnel to high intensity jet aircraft noise, which was the forerunner of the 1956 Air Force Regulation [Ref. 8] on "Hazardous Noise Exposure". A more recent application is the development of CNEL (Community Noise Equivalent Level) measure for describing the noise environment of airports. This measure, contained in the Noise Standards, Title 4, Subchapter 6, of the California Administrative Code (1970) is based upon a summation of Leq over a 24-hour period with weightings for exposure during evening and night periods

The Equivalent Noise Level was introduced in 1965 in Germany as a rating specifically to evaluate the impact of aircraft noise upon the neighbors of airports. [Ref. 9] It was almost immediately recognized in Austria as appropriate for evaluating the impact of street traffic noise in dwellings [Ref. 10] and in schoolrooms. [Ref. 11] It has been embodied in the National Test Standards of both East Germany [Ref. 12] and West Germany [Ref. 13] for rating the subjective effects of fluctuating noises of all kinds, such as from street and road traffic, rail traffic, canal and river ship traffic, aircraft, industrial operations (including the noise from individual machines), sports stadiums, playgrounds, etc. It is the rating used in both the East German [Ref. 14] and West German [Ref. 15] standard guidelines for city planning. It was the rating that proved to correlate best with subjective response in the large Swedish traffic noise survey of 1966-67. It has come into such general use in Sweden for rating noise exposure that commercial instrumentation is currently available for measuring Leq directly; the lightweight unit is small enough to be held in one hand and can be operated either from batteries or an electrical outlet. [Ref. 16]

The concept of representing a fluctuating noise level in terms of a steady noise having the same energy content is widespread in recent research, as shown in the EPA report on Public Health and Welfare Criteria for Noise (1973). There is evidence that it accurately describes the onset and progress of permanent noise-induced hearing loss, [Ref. 17] and substantial evidence to show that it applies to annoyance in various circumstances. [Ref. 18] The concept is borne out by Pearsons' experiments [Ref. 19] on the trade-off of level and duration of a noisy event and by numerous investigations of the trade-off between number of events and noise level in aircraft flyovers. [Ref. 20] Indeed, the Composite Noise Rating [Ref. 21] is a formulation of Leq, modified by corrections for day vs. night operations. The concept is embodied in several recommendations of the International Standards Organization, for assessing the noise from aircraft, [Ref. 22] industrial noise as it affects residences, [Ref. 23] and hearing conservation in factories. [Ref. 24]

COMPUTATION OF EQUIVALENT SOUND LEVEL

In many applications, it is useful to have analytic expressions for the equivalent sound level Leq in terms of simple parameters of the time-varying noise signal so that the integral does not have to be computed. It is often sufficiently accurate to approximate a complicated time-varying noise level with simple time patterns. For example, industrial noise can often be considered in terms of a specified noise level that is either on or off as a function of time. Similarly, individual aircraft or motor vehicle noise events can be considered to exhibit triangular time patterns that occur intermittently during a period of observation. (Assuming an aircraft flyover time pattern to be triangular in shape instead of shaped like a "normal distribution function" introduces an error of, at worst, 0.8 dB). Other noise histories can often be approximated with trapezoidal time pattern shapes.

The following sections provide explicit analytic expressions for estimating the equivalent sound level in terms of such time patterns, and graphic design charts are presented for easy application to practical problems. Most of the design charts are expressed in terms of the amount that the level (L) of the new noise source exceeds an existing background noise level, Lb. This background noise may be considered as the equivalent sound level that existed before the introduction of the new noise, provided that its fluctuation is small relative to the maximum value of the new noise level.

Constant Level Noise -- Steady or Intermittent

The Leq for a continuous noise having a constant value of Lmax is Leq = Lmax, which is derived from

When Lmax is intermittently on during the period T for a fraction x of the total time, with a background noise level Lb present for the time fraction (1 - x), Leq is given by:

Where DL = Lmax - Lb. This pattern is illustrated and the expression is plotted in Figure A-1 for various values of L and x. For values of Lmax that are 10dB or more higher than Lb, Leq is approximated quite accurately by:

Leq = Lmax + 10 log x (dB) (Eq. A-5)

Except in extreme cases as noted on the graph. An hourly equivalent sound level (Lh) can be computed from the last equation with the integration time (T) equal to 3600 seconds (1 hour). An example of the relationship between Lh and Lmax as a function of pulse duration t for Lmax - Lb greater than 10 is given in Figure A-2. These results may be described by:

Lh = Lmax + 10 log t - 35.6 (dB) (Eq. A-6)

for (Lmax - Lb) > 10.

Triangular Time Patterns

The equivalent sound level for a single triangular time pattern having a maximum value of Lmax and rising from a background level of Lb is given by:

Except in extreme cases as noted on the graph. The value of Leq for a series on n identical triangular time patterns having maximum levels of Lmax is given by:

Where the duration between (Lmax - 10 dB) points* [*The duration for which the noise level is within 10 dB of Lmax; also called the "10 dB down" duration.] is T seconds, the background level is Lb, and the total time period is T. (See Figure A-3). A design chart for determining Leq for different values of DL as a function of Nt per hour is provided in Figure A-3.

Figure A-1. Leq for intermittent Lmax added to Lb. [Ref. 25]

Figure A-2. Hourly equivalent sound level as a function of pulse duration and maximum sound level for one pulse per hour of a succession of n shorter pulses having a total of the indicated duration during one hour. (Background sound level less than 30 dB). (Derived from Equation A-5).

Figure A-3. Leq for a repeated series of n triangular signals overlaid on a background level of Lb, dB and T = duration at (Lmax - 10) dB in seconds. [Ref. 25] (See Equation A-9).

An approximation to equation (A-9) for cases where L is greater than 10 dB is given by:

This equation yields fairly good results except in extreme cases as can be seen in the graph.

Trapezoidal Time Patterns

The equivalent sound level, Leq, for a trapezoidal time pattern having maximum level of Lmax, background level Lb, duration between (Lmax - 10 dB) points of T and duration at Lmax of § is given by

The approximation to Leq when (DELTA)L is greater than 10 dB, for § small compared to T, is:

This equation yields adequate results except in extreme cases as noted on the graph. Noting the similarity between equations (A-5) (A-8), and (A-12), one can approximate Leq for a series of trapezoidal pulses by suitably combining design data from Figure A-1 and A-3. That is, the approximate Leq for a series of n trapezoidal pulses is obtained by the Leq value for triangular pulses plus an additional term equal to 10 log n, e.g.,

Time Patterns of Noise Having a Normal Statistical Distribution

Many cases of noise exposures in communities have a noise level distribution that may be closely approximated by a normal statistical distribution. The equivalent sound level for the distribution can be described simply in terms of its mean value, which for a normal distribution is L50, and the standard deviation (s) of the noise level distribution:

Leq = L50 + 0.115 s2 (dB) (Eq. A-14)

A design chart showing the difference between Leq and L50 as a function of the standard deviation is provided in Figure A-4.

It is often of interest to know which percentile level of a normal distribution is equal in magnitude to the Leq value for the distribution. A chart providing this relationship as a function of the standard deviation of the distribution is provided in Figure A-5.

Various noise criteria in use for highway noise are expressed in terms of the L10 value. For a normal distribution, the L10 value is specified in terms of the median and the standard deviation by the expression L10 = L50 + 1.28 s. The difference between L10 and Leq is given by L10 - Leq = 1.28 s - 0.115 s.2 This expression is plotted as a function of s in Figure A-6.

It should be noted that traffic noise does not always yield a normal distribution of noise levels, so caution should be used in determining exact differences between Leq and L10.

RELATIONSHIPS BETWEEN DAYTIME AND NIGHTTIME EQUIVALENT SOUND LEVELS

The day-night sound level (Ldn) was defined as the equivalent A-weighted sound level during a 24-hour time period with a 10 decibel weighting applied to the equivalent sound level during the nighttime hours of 10 p.m. to 7 a.m. This may be expressed by the equation:

where

Ld = Leq for the daytime (0700-2200 hours)

and

Ln = Leq for the nighttime (2200-0700 hours).

Figure A-4. Difference between Leq and L50 for a normal distribution s having standard deviation of s. [Ref. 25] (See Equation A-14).

Figure A-5. Percentile of a normal distribution that is equal to Leq. [Ref. 25] (See Equation A-14 and Probability Function).

Figure A-6. Difference between L10 and Leq for a normal distribution. [Ref. 25]

Figure A-7. Comparison of the difference between day and night values of the equivalent sound level with the day-night average sound level, Ldn. [Ref. 25]

The effect of the weighting may perhaps be more clearly visualized if it is thought of as a method that makes all levels measured at night 10 dB higher than they actually are. Thus, as an example, if the noise level is a constant 70 dB all day and a constant 60 dB all night, Ldn would be 70 dB.

Methods for accounting for the differences in interference or annoyance between daytime/nighttime exposures have been employed in a number of different noise assessment methods around the world. [Ref. 5] The weightings applied to the nondaytime periods differ slightly among the different countries but most of them weight night activities on the order of 10 dB; [Ref. 24] the evening weighting if used is 5 dB. The choice of 10 dB for the nighttime weighting made in Section 2 was predicated on its extensive prior usage, together with an examination of the diurnal variation in environmental noise. This variation is best illustrated by comparing the difference between Ld and Ln as a function of Ldn over the range of environmental noise situations.

Data from 63 sets of measurements were available in sufficient detail that such a comparison could be made. These data are plotted in Figure A-7. The data span noise environments ranging from the quiet of a wilderness area to the noisiest of airport and highway environments. It can be seen that, at the lowest levels (Ldn around 40-55 dB), Ld is the controlling element in determining Ldn, because the nighttime noise level is so much lower than that in the daytime. At higher Ldn levels (65-90 dB), the values of Ln are not much lower than those for Ld; thus, because of the 10 dB nighttime weighting, Ln will control the value of Ldn.

The choice of the 10 dB nighttime weighting in the computation of Ldn has the following effect: In low noise level environments below Ldn of approximately 55 dB, the natural drop in Ln values is approximately 10 dB, so that Ld and Ln contribute about equally to Ldn. However, in high noise environments, the night noise levels drop relatively little from their daytime values. In these environments, the nighttime weighting applies pressure towards a round-the-clock reduction in noise levels if the noise criteria are to be met.

The effect of a nighttime weighting can also be studied indirectly by examining the correlation between noise measure and observed community response in the 55 community reaction cases presented in the EPA report to Congress of 1971. [Ref. 1] The data have a standard deviation of 3.3 dB when a 10 dB nighttime penalty is applied, but the correlation worsens (std. dev. = 4.0 dB) when no nighttime penalty is applied. However, little difference was observed among values of the weighting ranging between 8 and 12 dB. Consequently, the community reaction data support a weighting of the order of 10 dB but they cannot be utilized for determining a finer gradation. Neither do the data support "three-period" in preference to "two-period" days in assigning nondaytime noise penalties.

Continued