## 1 Introduction
The approximation is based on experimental data between 30% and 80% relative humidity and limited to a fixed air temperature of 20 \({}^{\circ}\)C. Nothing is said about the bandwidth of the measurements. Obviously, the attenuation is assumed to be a simple linear function of the frequency, which is not true for measurements in octave bands but can be an acceptable approximation for one-third octave bands. Again, there is no evidence of a general application of the method in practice. A very precise analysis of the problem with air absorption and octave bands was presented by [PERSON] and [PERSON] [7]. They describe how the air absorption shapes the spectrum such that, after some time of propagation, most of the energy is in the lower part of the band. A numerical calculation method is presented, where the octave band is divided into a number of constant percentage filter elements. It is suggested that the number of filter elements must be at least 12 for an integration error less than 0.1 dB. [PERSON] and [PERSON] [8] simulated the effect of one-third octave band filters used for reverberation time measurements. They found that the results will differ significantly from those of a pure tone with a frequency at the geometric center of the band. They mention that octave band filters would lead to even greater differences. ISO 9613-1 [1] is the reference for calculating the absorption of sound by the atmosphere. The energy attenuation coefficients calculated in accordance with the standard are provided in tables with the pure-tone attenuation coefficients at the exact center frequencies of one-third octaves from 50 Hz to 10 kHz, temperatures from \(-20\)\({}^{\circ}\)C to \(+50\)\({}^{\circ}\)C in 5\({}^{\circ}\)C intervals, and relative humidity from 10% to 100% in 10% intervals. In addition, the exact formulas behind the calculations are provided. In the standard, it is stated that the exact midband frequency of an octave band can be used for an approximate calculation of the air attenuation of broadband sound in an octave band. This is applicable when the attenuation due to air absorption is not more than approximately 15 dB. The error is \(\leq\)\(\pm\)0.5 dB for \(r\cdot(f_{\rm c})^{2}\leq 3\) km (kHz)\({}^{2}\), where \(r\) is the distance of sound propagation and \(f_{\rm c}\) is the center frequency. The standard is intended for outdoor sound propagation, but there should be no problem in applications for sound propagation in rooms. In rooms with hard surfaces, the reverberation time may exceed 8 s at some frequencies. This means that, for room acoustical applications, the simple approximation using the center frequency may be valid below 1 kHz but not in octave bands above 1 kHz. The American National Standard ANSI S1.26 [9] has contents almost identical to ISO 9613-1 [1]. However, an approximate method for fractional-octave bands is described in [9] (Annex E). It is a non-linear function of the pure-tone attenuation at the midband frequency over the total distance of sound propagation. The approximate attenuation is calculated as the product of the pure-tone attenuation of the exact center frequency and a non-linear function or this pure-tone attenuation and the normalized filter bandwidth. ISO 9613-2 [10] is a standard describing calculation methods for outdoor sound propagation. In [10] (Chapter 7.2), typical examples of attenuation coefficients for octave bands of noise in dB/km are presented. Ref. [10] (Table 2) provides data for octave bands from 63 Hz to 8000 Hz. The data are the pure-tone attenuation coefficients of the octave band center frequencies. This implies, according to [8] (8.1.3), that the data are not accurate for attenuations above 15 dB. In the 8 kHz band, the maximum distance of valid application is found to be between 74 m and 253 m in the examples in [10] (Table 2). It is noted that these limitations of application are not mentioned in the standard.