Evaluations of the Annoyance Effects of Noise

Noise is defined as audible sound that disrupts silence and causes annoyance. The traditional way of assessing the annoying effect of noise is to determine its level on an A-weighted decibel scale. Such a scale was introduced in 1961, making it possible to estimate the loudness level of perceived noise [1]. This international standard (ISO-226) was modified in 2003 and introduced in Russia in 2009. However, the A‑weighted scale had disadvantages: it gave large errors in assessing the loudness levels of tonal, pulsed, and predominantly low-frequency noise, and was unsuitable for measuring peak sound pressure level (SPL) values. Therefore, first in 1967, a regional German standard (DIN 45631) [2] was introduced, then in 1975 the international standard (ISO 532) [3] for calculating the loudness of sounds in linear units, sones. The standard has changed several times and currently has two parts. The first part describes the method for calculating the loudness of sound perceived by listeners with normal hearing, which was proposed by Zwicker [4, 5], and the second, by Moore and Glasberg [6, 7]. The methods are suitable for calculating the loudness of tonal sounds, broadband and narrowband noise, and complex sounds. Zwicker’s method is for stationary sounds; the Moore–Glasberg method, for time-varying (nonstationary) sounds, including a particular case of stationary sounds. The latter method also makes it possible to calculate binaural loudness and reproduce equal loudness curves [1] and reference hearing thresholds [8]. The use of loudness calculation methods does not require special knowledge about the properties of auditory perception of sounds. Different methods evaluate the loudness of similar sounds differently, but none of the methods has any particular advantage: users choose the method they need. In Russia, a standard for calculating the loudness of sounds [3] has not been introduced.

The loudness scale of noise in sones does not fully correspond to the scale of loudness levels in dB(A) (Fig. 1). Thus, the loudness of a violin in sones is less than that of an electric drill, but the loudness level of a violin in dB(A), on the contrary, is higher than that of an electric drill. The same situation is with the sounds of a lawn mower and a pipe. The straight lines in Fig. 1 emphasize the loudness and loudness levels of normal speech. The range of loudness levels of sounds that exceed the level of normal speech is compressed on the A-weighted scale compared to the loudness range on a linear scale. Due to the compression, the differences in the loudness levels of the compared sounds in dB(A) can be within the measurement error, and estimates of the differences in the induced annoyance can be inaccurate. Therefore, standards for loudness calculations were developed and devices for measuring the loudness of sounds in sones appeared.

Normalization of the harmful effects of sounds goes beyond the standards for loudness calculations. In Russia, such norms are established by health regulations [9]. According to the regulations, the permissible noise level in subway passenger cars and the driver’s cab is quite high, 75 dB(A).

Annoyance, in addition to loudness, can cause other subjective noise qualities. In psychoacoustic studies, subjective qualities independent of each other have been identified: sharpness, fluctuation strength, roughness, tonality, etc. [10]. For these, measures and units of measurement have been determined, models of auditory perception of qualities; methods for calculating quality metrics were developed, national and international standards for calculation methods have been introduced [1‐3, 11‐13]. In Russia, standards for calculating sound qualities have not been introduced.

There are no acceptable standards for the sound quality metrics. That is why to identify pleasant and unpleasant noise components for their subsequent amplification or leveling, the metric short-term psychoacoustic annoyance (PAA) was introduced, which takes into account different metrics of qualities [10]. It was obtained in research on the perception of various types of synthetic noise.

Another way to assess annoyance and highlight annoying noise components is to construct a model that relates the result of auditory ranking of noise by degree of annoyance (SQ rank) with metrics of the subjective qualities of these noise [14]. Such a relationship model is obtained once prior to developing a noise reduction plan and is used in execution of the plan to predict noise annoyance and determine the contributions of different noise qualities to the annoyance.

This paper compares different methods for assessing noise annoyance by measuring loudness levels (dB(A)) and loudness (sones), as well as measuring the metrics of the subjective qualities of noise. As examples, the noise recorded in Moscow subway cars was used.

First, we briefly describe what is meant by the subjective qualities of sounds.

The human auditory system divides perceived sounds into frequency groups, which in the German school of psychoacoustics are called critical bands [5, 10]. It is accepted that in the range of audible frequencies there are 24 bands adjacent to each other on a scale from 0 to 24 Barks (critical band rate). The widths of such bands for tones with frequencies less than 500 Hz are approximately constant and equal to 100 Hz, and for tones with frequencies above 500 Hz, they increase in proportion to frequency. There is also another known scale. According to the English school of psychoacoustics, the scale has 40 frequency groups, called rectangular bands, which are equivalent to auditory bands (ERB rate) [7]. The widths of all such bands are proportional to the center frequencies. The formation of the subjective qualities of sounds is based on the concept of auditory critical bands (CB) or equivalent rectangular bands (ERB).

An important subjective quality of sounds is loudness (L) [5, 10], which characterizes the subjective perception of the strength/intensity of sound. The unit of measure for loudness is the sone. A loudness of 1 sone corresponds to the standard: a sinusoidal tone with a frequency of 1 kHz and level of 40 dB.

Loudness depends complexly on the pressure (intensity), duration, and frequency of sound. The loudness is the higher, the greater the intensity, duration, and spectral width of sound [15]. When forming loudness, the initial part of the sound is more important than its subsequent parts [16, 17]. This “initial” effect does not depend on the duration of the sound; it occurs when sounds issue in silence and in the presence of noise [18]. Sounds are louder when listening through two ears. The effect is called binaural loudness summation [19, 20].

Based on calculations of loudness L sounds lies the summation of specific loudnesses L', which are calculated in sets of CB or ERB and which are related by a power law with changes in perceived intensity [4]. As stated above, the loudness calculation standard [3] has been adopted.

The subjective quality of sharpness (S) of sound is perceived separately from loudness [10]. Higher-frequency noise is perceived as more unpleasant, aggressive, and annoying than lower-frequency noise of equal loudness. Sharpness is related to perception of the spectral envelope of sound. It is compared to the “center of gravity” of sound: the higher the center of gravity on the frequency scale, the sharper the sound.

The unit of measure for sharpness is the acum. The reference sound of 1 acum corresponds to narrowband noise with a level of 60 dB, a center frequency of 1 kHz, and a bandwidth not exceeding 150 Hz. The sensation of sharpness correlates with the sensation of loudness: the greater the loudness, the sharper the sound. With an increase in sound level from 30 to 90 dB, the sharpness approximately doubles. However, if the difference in levels of the compared sounds is not large, then the relationship between sharpness and sound level is neglected.

The method for determining sharpness S calculates the specific sound loudnesses in sets of CB. The overall sharpness is the ratio of the convolution integral of the specific loudness with a weighting factor g to the total sound loudness [10]. Weighting coefficient g is associated with the number of CB and is equal to one for numbers of CB less than 16 Barks, but increases to 4 in proportion to an increase in the number of CB from 16 to 24 Barks.

Sound modulations cause differing and independent auditory sensations (subjective qualities) [10]. At very low AM frequencies (less than 20 Hz), listeners experience changes in sound loudness. These sensations are associated with the subjective quality of sound, called the fluctuation strength (FS). The maximum sensation of FS occurs under the action of tones, as well as broadband and narrowband noise, with a modulation frequency of 4 Hz.

The unit of measure for FS is the vacil. A sensation of 1 vacil is induced by a 100% sinusoidal amplitude modulated (AM) tone with a carrier frequency of 1 kHz, a modulation frequency of 4 Hz, and an intensity of 60 dB. With an increase in the sound pressure level of modulated sounds from 40 to 80 dB, FS increases by ~2.5 times. The dependence of FS on the carrier frequency is weak for AM tones, but more appreciable for frequency modulated (FM) tones. Narrowband unmodulated noise possesses FS. In this case, FS is determined by the bandwidth of noise dF, and the effective modulation frequency f_mod is ~0.64 dF.

The metrics of FS calculated according to auditory model [10], which takes into account the change in time of the auditory masking profile of a test pulse presented against a 100% AM tone (noise) background. The masking profile corresponds to the dependence of the pulse detection threshold on the occurrence time of the pulse in the tone modulation period and detects a change in the loudness of the test pulse in the presence of noise. The shape of the profile is affected by the pre-, simultaneous, and postmasking processes. The profile determines the depth of auditory masking ΔL, which is equal to the difference between the maximum and minimum values of the detection thresholds. The expression for determining the metric FS looks as follows:where ∆L—is the depth of auditory masking; f_mod— interference modulation frequency. It is believed [10] that at frequencies f_mod > 4Hz, sensation FS is formed under the influence of temporary masking effects, and at frequencies f_mod < 4 Hz, under the influence of short-term memory. Under the action of broadband AM noise or complex AM and FM sounds, in calculating the metric FS, instead of masking depth ΔL, the sum of masing depths ΣΔL obtained in the set of sound-excited CB are taken into account.

At modulation frequencies exceeding 15–20 Hz, listeners, instead of feeling the fluctuation strength (FS), experience another sensation: roughness (R) [10]. The maximum roughness sensation occurs under the action of a 100% AM tone with a carrier frequency of 1 kHz and modulation frequency of 70 Hz. At modulation frequencies of 150 Hz and above, the roughness sensation is reduced and the listener hears three separate tones.

The unit of measure for roughness is the asper. 1 asper corresponds to sensation of a 100% sine wave AM tone with a carrier frequency of 1 kHz, modulation frequency of f_mod at 70 Hz, and an intensity of 60 dB.

For 100% AM tones, the dependence of roughness R on the modulation frequency f_mod has a hump, the magnitude of which depends on the carrier frequency f_c. The largest hump is recorded at f_c at 1 kHz and f_mod at 70 Hz.

The dependence of roughness on the modulation frequency for broadband AM noise coincides with that obtained for AM and FM tones with high frequencies f_c (more than 1 kHz). The maximum roughness also falls on f_mod at 70 Hz, regardless of the noise bandwidth and type of its modulation.

Narrowband noise sounds rough due to random changes in the envelopes. Noise with a band of 100 Hz and frequency f_mod at 64 Hz has the most significant roughness. In addition, roughness is inherent in sounds the envelopes of which do not have periodic modulation, but the spectra have peaks in the range of 15–300 Hz.

With an increase in sound pressure level by 40 dB, roughness R increases by about three times, as does the fluctuation strength FS. A change in roughness is felt with an approximately 10% increase in modulation depth. Sounds with frequency rather than amplitude modulation have a greater roughness. The roughness of sounds with frequency modulation in the entire auditory frequency range can reach ~6 aspers. Broadband AM noise can have the same roughness.

The models for calculating the fluctuation strength FS and roughness R are similar [10, 21]. The roughness model is also based on temporal masking profiles that determine the masking depth ΔL. At the same time, roughness R is proportional to the product f_mod × ΔL. This product has the maximum value at frequencies f_mod ~70 Hz, but decreases with a decrease in f_mod below 70 Hz (despite an increase in ΔL) and an increase in f_mod above 70 Hz owing to a reduction in the temporal resolution of loudness and ΔL tending to zero.

In calculating the roughness metric R of complex AM and FM sounds, as well as broadband noise, instead of the masking depth ΔL, the sum of the masking depths ΣΔL calculated in the set of sound-excited CB is used.

Another subjective quality of noise that can cause annoyance is key (tone T). This term appeared in the 19th century to describe pitch organization of sounds in music. In acoustics, this term has a different meaning. Sound is perceived as tonal if it contains a pronounced frequency component. Noise with tonal components, depending on their properties, can be both pleasant and annoying.

Typically, tonality is estimated from the weight of the tonal components in the noise spectrum. Weight calculations involve comparing the amplitude of some tonal component with the amplitudes of neighboring components. To quantitatively assess tonality, the tone-to-noise ratio or perceptibility metric is used. Such metrics do not take into account the peculiarities of auditory processing, so Sottek proposed a “psychoacoustic” method for calculating tonality [22, 23].

Tonality was calculated with an auditory perception model for pitch, including estimation of the total loudness as the sum of specific loudnesses in the set of CB and with account of audibility thresholds and auditory masking effects. The calculation involved comparison of loudness in one CB with loudness in the adjacent CB. The unit of measure tu or tuHMS was chosen to assess tonality: “tu” from the English word turbidity and HMS from the English combination of the Hearing Model by Sottek. On the tonality scale HMS 1 tu characterizes sound with a strongly pronounced and highly annoying tonality; 0.5 tu, a sound with a pronounced and annoying tonality; 0.1 tu, a sound with a weak and nonannoying tonality. The method for calculating tonality is presented in the ECMA-74 standard, which regulates the noise of IT equipment [13].

The overall sound quality of noise, whether pleasant or annoying, is judged by the listener. The listener’s attitude to noise is determined not only by subjective qualities, but also by his aesthetic and cognitive preferences, as well as his psychophysiological state. It is difficult to evaluate the latter factors, but it is possible to take into account the peculiarities of perception of the acoustic characteristics of sounds, describing them as a combination of subjective qualities. Taking into account these qualities, a quantitative expression was introduced to analyze short-term psychoacoustic annoyance (PAA) [10]. The expression was obtained from the results of auditory experiments on perception of synthetic modulated and unmodulated noise differing in their spectral content. The relationship between the PAA metrics and metrics of loudness L, sharpness S, fluctuation strength FS, and roughness R obtained for given noise had the following form:where L is the 5th percentile loudness in sone;

The PAA metrics is in demand at the product design stage. This is especially true for articles that generate intense noise (e.g., for aircraft), when it is necessary to compare different approaches to choosing product design and materials [24, 25] or a calculated forecast of product noise is possible [26, 27], but time-consuming auditory examination of predicted noise is still unsuitable. Therefore, to quantitatively estimate the annoying effect of aircraft noise, the PAA metrics was modified [28]. It took into account not only the above metrics L, S, FS and R, but also a tonality metrics T, which is quite annoying for aircraft noise:where: γ₀ = 0.16, γ_S = 11.48, γ_FSR = 0.84, γ_T = 1.25;

W_T = (1 - e–0.29L) (1 - e–5.49T); W_S and W_FSR are the same as in formula (2).

A more universal and widely used method for assessing noise annoyance, used at the development and improvement stage for a variety of products from coffee makers to wind turbines, involves creation of a mathematical model that relates the subjective opinion of auditory experts on noise quality with the calculated quality metrics of such noise [14]. To construct such a relationship model, a set of noise is initially formed and metrics of subjective qualities are calculated for them. Next, auditory experts are recruited and trained, who then rank the selected noise according to the degree of annoyance induced.

To rank noise, one of three methods is most often used: (1) the pairwise comparison method, (2) the category–judgment method, and (3) the semantic differential method. The first involves comparing pairs of noise and selecting the noise with the best given quality. Based on the results of the comparison, the noise from the set is assigned ranks proportional to the number of preferences. The advantage of the method is its simplicity and the ability to include model noise to determine annoyance characteristics. A drawback is the complexity of ranking a large number of noise, since the listener listens to the same pair of sounds repeatedly to check the consistency of the results.

The category–judgment method involves listening to sounds once, and the expert, e.g., on a scale of 1–10, determines how loud, sharp, unpleasant, etc., the sound was. In order to categorize noise in terms of annoyance, listeners should be a priori familiar with the noise being tested.

The semantic differential method is similar to the category–judgment method, but instead of evaluating the properties of a sound using one category (e.g., loud noise), the listener is asked to choose from a pair of categories with opposite attributes, e.g., from the pair of loud versus quiet.

Based on the results of the auditory examination, a scale of annoyance of a given noise set is formed. Each noise is assigned an auditory rank (SQ rank), which is related to the calculated noise quality metrics (L, S, R, FS). The relationship model is obtained by multiple linear regression methods in the form:where b₁, b₂, b₃, b₄ and b₀ are the regression coefficients.

At the next stage, statistical analysis of the quality of the relationship model is carried out and the reliability of the regression coefficients is evaluated. A properly constructed relationship model (Eq. (4)) includes a unique combination of statistically significant subjective noise qualities that cause annoyance. This equation helps in planning measures to correct the noise of specific articles or ambient medium and makes it possible to control the degree of annoyance in implementing the plan of action.

To compare different ways of estimating annoyance, the noise of Moscow subway cars was used. Noise was recorded in different modes of operation of the cars: idling or in motion, and during operation of systems: engine, air conditioner, compressor. The duration of the records was several minutes. The time profiles of noise were nonstationary and had pronounced components caused by vibrations during wheel–rail interaction (Fig. 2).

Integrated sound pressure levels (SPL) without (dB(lin)) and with A-weighting (dB(A)) were measured from fragments of records of such noise that did not contain wheel knocking with an accumulation time of 1 s. Table 1 shows the numbers of noise in different modes of operation of cars, a description of the modes, and the measured SPL of the noise.

To analyze the loudness and other qualities of the noise, the recordings were converted into WAV format normalized according to the peak values inherent in wheel knocking. From each record, four to five stationary segments were cut out that did not contain wheel knocks. The duration of segments was ~3 s. Examples of spectrograms of such noise segments are shown in Fig. 3. The frequency characteristics of the segments were broadband and had well-pronounced low-frequency components.

Standard methods exist [8‐13] for calculating the sound quality metrics; these are implemented in software products from different companies and can be used to develop proprietary programs. In this study, the quality metrics were calculated in the LabVeiw environment.

The objective of the study was to compare different methods for analyzing the annoying effect of noise. In Russia, the classic method for estimating annoyance is to measure the SPL of noise in dB(A), which roughly corresponds to the perceived loudness level. However, this method may only be suitable for certain types of noise. A more universal integral method to measure and calculate the noise loudness in linear units of sones, but this method has not found application in Russia.

Loudness measurements are used in implementing measures to reduce noise below acceptable limits. However, the informational significance of noise, as well as the already achieved significant reduction in the levels of the latter, led to other methods for assessing noise-induced annoyance that complement the traditional method. These include calculation of short-term psychoacoustic annoyance (PAA) based on different subjective noise qualities, as well as auditory examination of annoyance (SQ rank) and construction of a relationship model between annoyance and the subjective qualities of noise responsible for it. These methods are aimed at determining the degree of annoyance and its causes. Taking into account the PAA metrics and relationship model SQ rank, plans can be developed to further reduce the noise levels of machines and mechanisms, mitigate their annoying effects, and create a given soundscape for rooms. The PAA metric and SQ rank are used to monitor the effectiveness of such plans.

The study shows the following

1. The linear loudness scale in sones is better suited for assessing loudness as a metric of the annoying effect of subway car noise than the A-weighted SPL dB(A) scale. The latter scale is widely used to assess perceived loudness levels; however, in the presence of low-frequency components in the noise spectra, such a scale may yield errors. In Russia, loudness measurements in sones are not widely used.

2. Annoyance, in addition to loudness, can cause other subjective noise qualities. Annoyance in subway cars can be assessed with metric of short-term PAA. This metric is calculated using various metrics of subjective qualities, including loudness, sharpness, roughness, and fluctuation strength. In Russia, annoyance assessments based on the PAA metric are not widely used.

4. The loudness of noise recorded in subway cars from several sources, i.e., engine plus air conditioner plus compressor, cannot be predicted by analyzing the loudness of noise from individual sources, i.e., only the engine, air conditioner, and compressor separately.