Relations among loudness, loudness level, and sound pressure level
Numerical analysis of loudness, loudness level, and sound-pressure level of pure tones of steady noise that does not exceed critical bandwidth
Howes, W. L.↗
SEARCH · Search NASA
Results for “loudness”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Loudness function derives from data on electrical discharge rates in auditory nerve fibers
Judgements of the loudness of pure-tone sound stimuli yield a loudness function which relates perceived loudness to stimulus amplitude. A loudness function is derived from physical evidence alone without regard to human judgments. The resultant loudness function is L=K(q-q0), where L is loudness, q is effective sound pressure (specifically q0 at the loudness threshold), and K is generally a weak function of the number of stimulated auditory nerve fibers. The predicted function is in agreement with loudness judgment data reported by Warren, which imply that, in the suprathreshold loudness regime, decreasing the sound-pressure level by 6 db results in halving the loudness.
Howes, W. L.↗
Effect of sonic boom asymmetry on subjective loudness
The NASA Langley Research Center's sonic boom apparatus was used in an experimental study to quantify subjective loudness response to a wide range of asymmetrical N-wave sonic boom signatures. Results were used to assess the relative performance of several metrics as loudness estimators for asymmetrical signatures and to quantify in detail the effects on subjective loudness of varying both the degree and direction of signature loudness asymmetry. Findings of the study indicated that Perceived Level (Steven's Mark 7) and A-weighted sound exposure level were the best metrics for quantifying asymmetrical boom loudness. Asymmetrical signatures were generally rated as being less loud than symmetrical signatures of equivalent Perceived Level. The magnitude of the loudness reductions increased as the degree of boom asymmetry increased, and depended upon the direction of asymmetry. These loudness reductions were not accounted for by any of the metrics. Corrections were determined for use in adjusting calculated Perceived Level values to account for these reductions. It was also demonstrated that the subjects generally incorporated the loudness components of the complete signatures when making their subjective judgments.
Leatherwood, Jack D.↗
Loudness enhancement and decrement in four paradigms
When one tone burst (the conditioner) preceeds another (the target) by 100 ms, target loudness is enhanced if the conditioner is more intense and decreased if it is less intense. We show here that similar loudness enhancements and decrements occur when the conditioner follows the target. In all instances, monaural loudness enhancements (in which the conditioner and target are delivered to the same ear) are greater than the dichotic enhancements (in which the conditioner is presented contralaterally), but the decrements, which are smaller than the enhancements, are similar in magnitude. Loudness enhancements and decrements are similar to sequential loudness effects and central tendency effects; the major difference is the relatively very large increases in loudness obtainable in loudness enhancement experiments. We outline a mechanism to account for these loudness phenomena and suggest that this mechanism is responsible for similar perceptual effects that occur in other stimulus dimensions and modalities.
Elmasian, R.↗
Subjective loudness response to simulated sonic booms
A series of laboratory studies were conducted at LaRC to: (1) quantify the effects of sonic boom signature shaping on subjective loudness; (2) evaluate candidate loudness metrics; (3) quantify the effects of signature asymmetry on loudness; and (4) document sonic boom acceptability within the laboratory. A total of 212 test subjects evaluated a wide range of signatures using the NASA Langley Research Center's sonic boom simulator. Results indicated that signature shaping via front-shock minimization was particularly effective in reducing subjective loudness without requiring reductions in peak overpressure. Metric evaluations showed that A-weighted sound exposure level, Perceived Level (Stevens Mark 7), and Zwicker's Loudness level were effective descriptors of the loudness of symmetrical shaped signatures. The asymmetrical signatures were generally rated as being quieter than symmetrical signatures of equal calculated metric level. The magnitude of the loudness reductions were observed to increase as the degree of asymmetry increased and to be greatest when the rear half of the signature was loudest. This effect was not accounted for by the loudness metrics. Sonic boom acceptability criteria were determined within the laboratory. These agreed well with results previously obtained in more realistic situations.
Leatherwood, Jack D.↗
Loudness of steady sounds - A new theory
A new mathematical theory for calculating the loudness of steady sounds from power summation and frequency interaction, based on psychoacoustic and physiological information, assuems that loudness is a subjective measure of the electrical energy transmitted along the auditory nerve to the central nervous system. The auditory system consists of the mechanical part modeled by a bandpass filter with a transfer function dependent on the sound pressure, and the electrical part where the signal is transformed into a half-wave reproduction represented by the electrical power in impulsive discharges transmitted along neurons comprising the auditory nerve. In the electrical part the neurons are distributed among artificial parallel channels with frequency bandwidths equal to 'critical bandwidths for loudness', within which loudness is constant for constant sound pressure. The total energy transmitted to the central nervous system is the sum of the energy transmitted in all channels, and the loudness is proportional to the square root of the total filtered sound energy distributed over all channels. The theory explains many psychoacoustic phenomena such as audible beats resulting from closely spaced tones, interaction of sound stimuli which affect the same neurons affecting loudness, and of individually subliminal sounds becoming audible if they lie within the same critical band.
Howes, W. L.↗
Loudness and annoyance response to simulated outdoor and indoor sonic booms
The sonic boom simulator of the Langley Research Center was used to quantify subjective loudness and annoyance response to simulated indoor and outdoor sonic boom signatures. The indoor signatures were derived from the outdoor signatures by application of house filters that approximated the noise reduction characteristics of a residential structure. Two indoor listening situations were simulated: one with the windows open and the other with the windows closed. Results were used to assess loudness and annoyance as sonic boom criterion measures and to evaluate several metrics as estimators of loudness and annoyance. The findings indicated that loudness and annoyance were equivalent criterion measures for outdoor booms but not for indoor booms. Annoyance scores for indoor booms were significantly higher than indoor loudness scores. Thus, annoyance was recommended as the criterion measure of choice for general use in assessing sonic boom subjective effects. Perceived level was determined to be the best estimator of annoyance for both indoor and outdoor booms, and of loudness for outdoor booms. It was recommended as the metric of choice for predicting sonic boom subjective effects.
Leatherwood, Jack D.↗
Relations among pure-tone sound stimuli, neural activity, and the loudness sensation
Both the physiological and psychological responses to pure-tone sound stimuli are used to derive formulas which: (1) relate the loudness, loudness level, and sound-pressure level of pure tones; (2) apply continuously over most of the acoustic regime, including the loudness threshold; and (3) contain no undetermined coefficients. Some of the formulas are fundamental for calculating the loudness of any sound. Power-law formulas relating the pure-tone sound stimulus, neural activity, and loudness are derived from published data.
Howes, W. L.↗
Loudness determined by power summation.
The predicted overall loudness of steady, broad-band noise is usually computed by summing weighted loudnesses of sub-bands of the noise intensity (mean-square pressure) spectrum. It is proposed, instead, that the overall loudness should be computed by summing weighted intensities of sub-bands ('critical bands') of noise and then obtaining the loudness of the sum. This method seems to yield better agreement with published loudness judgments than does the usual method. It appears that the proposed method should also yield better agreement with annoyance judgments than does the 'perceived noise' method of Kryter.
Howes, W. L.↗
Contribution of tonal components to the overall loudness, annoyance and noisiness of noise: Relation between single tones and noise spectral shape
A large scale laboratory investigation of loudness, annoyance, and noisiness produced by single-tone-noise complexes was undertaken to establish a broader data base for quanitification and prediction of perceived annoyance of sounds containing tonal components. Loudness, annoyance, and noisiness were distinguished as separate, distinct, attributes of sound. Three different spectral patterns of broadband noise with and without added tones were studied: broadband-flat, low-pass, and high-pass. Judgments were obtained by absolute magnitude estimation supplement by loudness matching. The data were examined and evaluated to determine the potential effects of (1) the overall sound pressure level (SPL) of the noise-tone complex, (2) tone SPL, (3) noise SPL, (4) tone-to-noise ratio, (5) the frequency of the added tone, (6) noise spectral shape, and (7) subjective attribute judged on absolute magnitude of annoyance. Results showed that, in contrast to noisiness, loudness and annoyance growth behavior depends on the relationship between the frequency of the added tone and the spectral shape of the noise. The close correspondence between the frequency of the added tone and the spectral shape of the noise. The close correspondence between loundness and annoyance suggests that, to better understand perceived annoyance of sound mixtures, it is necessary to relate the results to basic auditory mechanisms governing loudness and masking.
Hellman, R. P.↗
A loudness calculation procedure applied to shaped sonic booms
Described here is a procedure that can be used to calculate the loudness of sonic booms. The procedure is applied to a wide range of sonic booms, both classical N-waves and a variety of other shapes of booms. The loudness of N-waves is controlled by overpressure and the associated rise time. The loudness of shaped booms is highly dependent on the characteristics of the initial shock. A comparison of the calculated loudness values indicates that shaped booms may have significantly reduced loudness relative to N-waves having the same peak overpressure. This result implies that a supersonic transport designed to yield minimized sonic booms may be substantially more acceptable than an unconstrained design.
Shepherd, Kevin P.↗
The effect of turbulence on the loudness of minimized sonic boom signatures
An important issue for shaped minimized sonic booms is whether turbulence-induced distortions will adversely affect the benefits gained by shaping. This question was considerably simplified by two recent results. The first is the finding that the loudness of sonic booms is well quantified by loudness. The second is that loudness of a shaped boom is dominated by the shock waves. The issue is now the effect of turbulence on weak (1 psf or less) sonic booms. Since it is clear that molecular relaxation effects have a significant effect on shock structure and loudness, turbulence effects must be examined in conjunction with relaxation-thickened shocks. This analysis must be directed toward loudness calculations and include all pertinent mechanisms.
Plotkin, Kenneth J.↗
Laboratory study of effects of sonic boom shaping on subjective loudness and acceptability
A laboratory study was conducted to determine the effects of sonic boom signature shaping on subjective loudness and acceptability. The study utilized the sonic boom simulator at the Langley Research Center. A wide range of symmetrical, front-shock-minimized signature shapes were investigated together with a limited number of asymmetrical signatures. Subjective loudness judgments were obtained from 60 test subjects by using an 11-point numerical category scale. Acceptability judgments were obtained using the method of constant stimuli. Results were used to assess the relative predictive ability of several noise metrics, determine the loudness benefits of detailed boom shaping, and derive laboratory sonic boom acceptability criteria. These results indicated that the A-weighted sound exposure level, the Stevens Mark 7 Perceived Level, and the Zwicker Loudness Level metrics all performed well. Significant reductions in loudness were obtained by increasing front-shock rise time and/or decreasing front-shock overpressure of the front-shock minimized signatures. In addition, the asymmetrical signatures were rated to be slightly quieter than the symmetrical front-shock-minimized signatures of equal A-weighted sound exposure level. However, this result was based on a limited number of asymmetric signatures. The comparison of laboratory acceptability results with acceptability data obtained in more realistic situations also indicated good agreement.
Leatherwood, Jack D.↗
Obscuration, orientation, and the infrared properties of radio-loud active galaxies
We report on a study of the mid- and far-infrared (MFIR) properties of several different classes of radio-loud active galactic nuclei (AGNs) using the IRAS database. Our goal is to try to improve the understanding of the possible relationships between the diverse classes of AGNs. The MFIR and radio properties of radio-loud AGNs are especially useful in this regard, since (excluding the blazar class, which we do not study here) the radio emission is thought to be emitted isotropically, and the radio and MFIR radiation should be much less affected by dust obscuration than radiation at shorter wavelengths. We have first compared samples of 3CR broad-line radio galaxies (BLRGs) and narrow-line radio galaxies (NLRGs) matched in radio flux and mean redshift. We find that the BLRGs are stronger than the NLRGs by a factor of 4-5 in their mid-IR emission but are similar to the NLRGs in the far-IR. This is qualitatively consistent with recent 'unification' models for NLRGs and BLRGs which invoke thermal MFIR emission from dusty 'obscuring tori,' but there may be an additional source of far-IR emission present in the more luminous broad-line objects (the radio-loud quasars) studied previously by Heckman, Chambers & Postman (1992). We have also compared samples of Fanaroff-Riley class I (FRI) and Fanaroff-Riley class II (FRII) radio galaxies matched in radio flux and redshift. The FRII galaxies are stronger MFIR emitters than the FRI galaxies by a factor of about 4. This is consistent with suggestions that the central engine in FRI galaxies produces relatively little radiant energy per unit jet power (expecially since we find that the weak MFIR emission from the FRI galaxies may not be powered by the AGN). Comparing samples of gigahertz-peaked spectrum (GPS) and compact steep spectrum (CSS) sources versus non-GPS-CSS sources, we find that the GPS-CSS and non-GPS-CSS sources have similar MFIR strengths. This suggests that the efficiency of the conversion of jet kinetic energy into radio emission is not much higher in the GPS-CSS sources, contrary to some theoretical predictions. Overall, we find that the MFIR and radio powers of all the classes of radio-loud AGNs we have studied correlate well with one another over a range of about 10(exp 3) in power. This is most naturally understood if the MFIR is primarily powered by the AGN in most highly luminous radio-loud AGNs. However, other processes (starbursts or the intracluster medium) may contribute significantly in the less radio-luminous radio galaxies.
Heckman, Timothy M.↗
On the Integration of Loudness Over Time for the Prediction of Single-Event Annoyance
Loudness is the quality of human perception that is most related to acoustic intensity and energy, however there is no agreed-upon way of integrating loudness over time for the prediction of noise-induced annoyance. Most noise metrics used today for aircraft certification and regulation employ the “Equal-Energy Hypothesis” (EEH) and sum the acoustical energy of one or more noise events over time to create a single metric value that represents the entire exposure. Using the EEH creates a natural tradeoff between the peak energy and the duration of a single noise event, the “hypothesis” being that this tradeoff optimally predicts annoyance in a wide variety of situations. This work proposes a strategy for integrating a loudness-like time series which is flexible in two ways: First, it includes a parameter b ∈ [0,1]. When b = 0, the metric will return the peak of the time series. At b = .5, the metric will behave in accordance with the EEH. At b = 1, the metric will penalize the duration of the sound more than the EEH would. Second, transformations are given so that the strategy can be computed from, or generate quantities in units analogous to, decibels (or phon), physical units (acoustic pressure/power), or perceptually-scaled units (sone). This approach is demonstrated on a dataset of annoyance responses to single events of UAV and road vehicle noise that is fit with an augmented linear regression. Analyses based on this integration of A-weighted level and the output of the “Zwicker” loudness model yield similar results: that subjects may have been slightly more sensitive to the durations of the events than the EEH would suppose, but that the EEH cannot be disproven using these data. The time-integrated metrics outperform both time-averaged and centile-based metrics.
Psychoacoustics↗
On the Integration of Loudness Over Time for the Prediction of Single-Event Annoyance
Loudness is the quality of human perception that is most related to acoustic intensity and energy, however there is no agreed-upon way of integrating loudness over time for the prediction of noise-induced annoyance. Most noise metrics used today for aircraft certification and regulation employ the “Equal-Energy Hypothesis” (EEH) and sum the acoustical energy of one or more noise events over time to create a single metric value that represents the entire exposure. Using the EEH creates a natural tradeoff between the peak energy and the duration of a single noise event, the “hypothesis” being that this tradeoff optimally predicts annoyance in a wide variety of situations. This work proposes a strategy for integrating a loudness-like time series which is flexible in two ways: First, it includes a parameter b ∈ [0,1]. When b = 0, the metric will return the peak of the time series. At b = .5, the metric will behave in accordance with the EEH. At b = 1, the metric will penalize the duration of the sound more than the EEH would. Second, transformations are given so that the strategy can be computed from, or generate quantities in units analogous to, decibels (or phon), physical units (acoustic pressure/power), or perceptually-scaled units (sone). This approach is demonstrated on a dataset of annoyance responses to single events of UAV and road vehicle noise that is fit with an augmented linear regression. Analyses based on this integration of A-weighted level and the output of the “Zwicker” loudness model yield similar results: that subjects may have been slightly more sensitive to the durations of the events than the EEH would suppose, but that the EEH cannot be disproven using these data. The time-integrated metrics outperform both time-averaged and centile-based metrics.
Psychoacoustics↗
Uncertainty Quantification for Empirical X-59 Sonic Boom Loudness Levels
Estimates of the total uncertainty for empirically determined loudness levels are documented when GRS (Ground Recording System) noise monitors are used to record X 59 sonic boom waveforms. The total uncertainty is characterized by combining nine different sources of uncertainty that may affect the apparent gain of the measurement chain. These uncertainty estimates are presented as expected measurement error relative to the true loudness level, and separate error estimates are provided for eight different noise metrics in which NASA has interest. The behavior of the Perceived Level (PL) metric is studied within the report body, while the total uncertainties for the seven other noise metrics are summarized in appendices for brevity. The effects of four sources of uncertainty are estimated simply from information found on hardware specification sheets provided by the manufacturer. However, mock acoustic recordings are created to estimate the effects of other sources because those effects are expected to induce spectral coloration, so they may vary with noise metric type and sound level. These sources are not well modeled by simple gain adjustments. Importantly, measurement error is computable when processing mock recordings since the true levels are knowable, which is not the case when processing data recorded in the field. Specifically, the true levels are knowable because the components of the mock recordings are separable – e.g., loudness levels of booms can be computed with or without superimposed background noise. Mock acoustic recordings also have the benefit of allowing analysis of sonic booms from vehicles that are not yet flying, like the X-59, since the mock recordings are created by combining vehicle-specific predicted waveforms with other audio sources. The estimates of total measurement error are documented as a function of the signal-to-noise ratio (SNR) of the loudness level, where the corrected SNR is computed while accounting for the effects of the method that is used to correct for background noise contamination when computing the noise metric values. The corrected SNR calculations used here can be applied to both mock recordings and in-field measurements, so the uncertainty of in-field recordings can be found using pre-computed lookup tables that identify the relationship between metric type, corrected SNR, and the expected measurement error.
Sonic Boom↗
Overall loudness of steady sounds
Loudness (in sones) and loudness level (in phons) of any sound that is steady for tenths of second can be calculated using computer program derived from new operational theory of loudness. Theory is constructed from psychoacoustic and physiological data on mammalian (monkey) auditory systems. Computer program permits prediction of loudness of any steady sound including, for example, transportation noises, machinery noises, and other environmental noises, with possible additional applications to broadcasting, sound reproduction, establishment and enforcement of noise laws.
Howes, W. L.↗