Simple loudness adaptation for pure tones was measured at frequencies from 0.125 to 16 kHz and at sensation levels from 5 to 60 dB. Sixteen young listeners with normal hearing participated in four experiments. Most of the loudness measurements were obtained by the method of successive magnitude estimation; some were also obtained by loudness matching. The two indices of loudness adaptation gave similar results. At all frequencies, loudness adaptation increased as sensation level decreased. After 6 min, average loudness declined at most frequencies by about 20% at 40-dB sensation level (SL) and by between 70% and almost 100% at 5-dB SL. Adaptation also increased with increasing frequency, and was especially marked at 16 kHz, where loudness declined more than 60% at a sensation level as high as 40 dB. Most of the adaptation occurred usually within the first 3 min of exposure, but loudness continued to diminish at a slower rate up to around 6 min. The dependence of loudness adaptation on frequency and level can be largely accounted for by the restricted-excitation-pattern hypothesis. Adaptation is assumed to take place when excitation is restricted to a narrow region of the cochlea. This hypothesis is supported by a quantitative analysis based on excitation patterns derived from measurements of masking.

Loudness adaptation was measured for pure tones at 4, 12, 14, and 16 kHz. In three experiments, a total of 87 young listeners judged--by the method of successive magnitude estimation--the loudness of the tones over a 6-min exposure period. Thresholds were measured by an adaptive 2IFC procedure. Although earlier measurements had shown that adaptation near threshold increases with frequency, these new data reveal that the increase is especially marked at higher sensation levels. Thus, at 40 dB SL, over a 6-min period loudness declined by 18% at 4 kHz and by 94% at 16 kHz. Moreover, the 4-kHz tone remained audible for all listeners throughout the 6-min exposure period whereas the 16-kHz tone became inaudible for two-thirds of them by the end of the exposure period. Listeners with relatively low thresholds (< 50 dB SPL) at 16 kHz showed much less adaptation at 14 kHz than at 16 kHz and much less than listeners with relatively high thresholds (> 50 dB SPL) at 16 kHz; this latter group showed strong adaptation at 14 kHz. The marked loudness adaptation of steady tones at very high frequencies and relatively high sensation levels is associated with a restricted spread of excitation in the auditory system resulting from the steep rise of the threshold curve at the highest audible frequencies.

Loudness measured by the method of absolute magnitude estimation is compared to loudness calculated in accordance with ISO 532 B [International Organization for Standardization, Geneva, 1966]. The measured and calculated loudness functions exhibit a similar pattern of loudness growth. Both measured and calculated loudness of a complex sound composed of a 1000-Hz tone and broadband noise is a nonmonotonic function of the overall SPL of the complex. The nonmonotonic loudness-growth pattern holds over a 30-dB range from 73.5 to 103.5. To facilitate understanding of the results, a single cycle of data is analyzed in detail. The analysis shows that loudness patterns produced in the auditory system by the tone–noise complex can account for the observed effects. Moreover, they show that the A-weighting and the loudness of the complex are negatively related. This inverse relation means that the A-weighted SPL is an inappropriate and misleading indicator of the loudness of sound combinations with heterogeneous spectral envelopes. Consequently, its suitability for noise control is diminished. A loudness meter that combines the spectral shapes of different sounds to produce an overall perceived magnitude offers greater promise.

The intensity jnd is often assumed to depend on the slope of the loudness function. One way to test this assumption is to measure the jnd for a sound that falls on distinctly different loudness functions. Two such functions were generated by presenting a 1000-Hz tone in narrow-band noise (925-1080 Hz) set at 70 dB SPL and in wideband noise (75-9600 Hz) set at 80 dB SPL. Over a range from near threshold to about 75 dB SPL, the loudness function for the tone is much steeper in the narrow-band noise than in the wideband noise. At 72 dB SPL, where the two loudness curves cross, the tone's jnd was measured in each noise by a block up-down two-interval forced-choice procedure. Despite the differences in slope (and in sensation level), the jnd (delta I/I) is nearly the same in the two noises, 0.22 in narrow-band noise and 0.20 in wideband noise. The mean value of 0.21 is close to the value of 0.25 interpolated from Jesteadt et al. [J. Acoust. Soc. Am. 61, 169-176 (1977)] for a 1000-Hz tone that had the same loudness in quiet as did our 72-dB tone in noise, but lay on a loudness function with a much lower slope. These and other data demonstrate that intensity discrimination for pure tones is unrelated to the slope of the loudness function.

One way to assess the relation between intensity discrimination and the slope of the loudness function is to measure the jnd for a sound that falls on two distinctly different loudness functions. Two such functions were generated by presenting a 1000-Hz tone in narrow-band noise (NBN, 925–1080 Hz) at 70 dB SPL and in wideband noise (WBN, 75–9600 Hz) at 80 dB SPL. Over a range from near threshold to about 75 dB SPL, the tone's loudness function is much steeper in the NBN than in the WBN. At 72 dB SPL, where the two loudness curves cross, we measured the tone's jnd in each noise by a two-interval forced-choice procedure. Despite the differences in slope (and in sensation level), the jnd was the same in both NBN and WBN. The value of ΔI/I was 0.22, which is close to that interpolated from Jesteadt, Wier, and Green [J. Acoust. Soc. Am. 61, 169–176 (1977)] for a 1000-Hz tone at the same loudness in quiet as our 72-dB tone in noise. These and other data suggest the possibility that the size of the jnd for intensity depends more on loudness magnitude than on the slope of the loudness function. [Supported by funds from the Medical Research Service of the VA to RH and by a grant (BMS 73-06944) from NSF to RT.]

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How can one best predict subjective ratings of noise magnitude loudness, noisiness, unacceptability, annoyance, etc.)? To answer this question we applied six sound-level weightings (A, B, C, D1, D2, and E) and five calculation systems (Mark VI, Mark VII, PNL, PNL with tone correction, and Zwicker's) to over 500 spectra from 23 different studies in which listeners judged noise magnitude, usually by a matching procedure. These spectra represented a wide variety of noises: aircraft, artificial, industrial, vehicular, household, etc. In general, the calculation systems predicted perceived magnitude with less variability and greater validity than the simple frequency weightings. Among the weightings the D's and E were better than B and C, with A falling in between. Among the calculation systems, Mark VI, Mark VII, and Zwicker's were about equal to one another and were better than PNL. Except for Zwicker's, the calculation systems were more accurate when the judged attribute was noisiness, acceptability, annoyance, or the like than when the attribute was loudness. [Research supported by the Office of Noise Abatement and Control, EPA.]

We have used Stevens' method of magnitude estimation in a number of classes and with individual observers to obtain estimates of the loudness of pure tones. These unpracticed observers give results that mimic the tone scale: They agree that approximately a 10-dB change in sound pressure corresponds to a twofold change in loudness. Such results convince the student of the distinction between loudness, a subjective magnitude, and intensity, a stimulus magnitude. Moreover, the consistency across groups of listeners means that untrained people are able to judge loudness ratios directly. It would then be appropriate and more informative to tell consumers about the loudness or noisiness of products by giving the relative positions of products on a true number scale of loudness, rather than by giving the positions of products on a logarithmic scale of acoustical output.

Only a few studies have been concerned with the measurement of the loudness of a 1000-cps tone in the presence of noise; and there is a considerable discrepancy among the results, especially at low sound intensities. The discrepancy appears to be due to biases in procedures. In order to determine the form of the masked-loudness function, a series of experiments, which were designed to reduce the biases to a minimum, was performed. It has been found that, by decreasing the procedural biases and by obtaining measurements under similar experimental conditions, the average of magnitude estimation and magnitude production can be used to corroborate the results of loudness matching. By combining the loudness-matching field with the one determined by magnitude estimation and magnitude production, the best estimate of the masked-loudness function is obtained. Two loudness curves are constructed, one for a 40-dB threshold shift and the other for a threshold shift of 60 dB. The form of these curves is in good agreement with the results of other investigations in which balanced procedures are followed. The theoretical implications of these data are examined. (Work supported by a contract between the U. S. Office of Naval Research and Syracuse University.)

In recent years, S. S. Stevens revitalized the discussion concerning the growth of sensation as a function of stimulus intensity by showing that the relationship can be described more adequately in terms of a power function suggested by Plateau than in terms of a logarithmic function derived by Fechner. The power function applied by Stevens to various sense modalities holds at medium and high sensation levels. At near threshold intensities, it appears to deviate from empirical data. Attempts have been made to correct the discrepancy by adding a constant in the intensity domain. It is shown that such a correction is inadequate and that an additive constant on the sensation continuum produces a better approximation of the experimental data. The derivation of the mathematical expression is followed by examples in which experimental and theoretical data obtained under various psychophysical conditions are compared. (Work supported by a contract between the Office of Naval Research and Syracuse University.)

The effect of several factors on the loudness estimation was explored in a series of experiments. It has been found that the numerical estimation of loudness ratios by listeners without auditory pathology depends on the sensation level, when the number assigned to the standard is kept constant, and on the number assigned to the standard when the sensation level is invariant. Only when the sensation level and the number are varied simultaneously in an appropriate way is it possible to maintain an approximately constant loudness function. The experiments have led to the determination of the loudness function near the threshold of audibility. In general. the results are in agreement with the data obtained by Robinson, Zwicker, Scharf. and J. C. Stevens and with those of S. S. Stevens at medium and high sensation levels. (Work supported by a contract between the Office of Naval Research and Syracuse University.)