Equal Loudness Contours Research Articles

Auditory sensitivity and equal loudness in the squirrel monkey (Saimiri sciureus).

The effects of the type of reinforcer on auditory sensitivity and equal-loudness data were determined in the squirrel monkey. The monkeys, restrained and provided with earphones, were conditioned to depress and hold a bar down in the presence of a stimulus light and then to terminate the holding response after onset of a tone. In Experiment 1, the specified behavior sequence postponed electric shock; in Experiment 2, a food reinforcer was dependent on bar release during the tone. The shape of the auditory sensitivity function and the acuity level at each frequency were the same for the two procedures. The audible frequency range extended from below 0.125 kHz (lowest frequency used) to 46 kHz. Sensitivity was maximum at 8 kHz. Latency of bar release following tone onset served as the basic data for constructing a family of equal-loudness contours. The type of reinforcer appeared not to be a determinant of either the shape of individual loudness contours or the pattern of family of equal-loudness functions. At the lower sound-pressure levels, the equal-loudness contours closely paralleled the threshold curves. At more-intense levels, the contours tended to flatten and depend less on frequency.

Pure-tone equal-loudness contours for standard tones of different frequencies

Six Ss made judgments of equal loudness by adjusting the intensity of comparison tones of 10 different frequencies. The comparison tones were presented diotically alternately with standaxd tones. Each standard tone remained fixed at one frequency (125, 1,000, or 8,000 Hz) and one intensity (10, 20, 40, or 70 dB sensation level)while collecting the data for any single equal-loudness contour. In this manner, families of equal-loudness contours were generated for each of the three standard frequencies. The contours for the 1,000-Hz standard were compared with those in the literature. The families of contours for the 125- and 8,000-Hz standards, determined by the same algorithm, differed in the spacing of the contours from the 1,000-Hz standard family as well as from each other. Implications for the reflexive, symmetric, and transitive properties of the equal-loudness relation axe discussed.

Replication of Frequency Response Aspects of Hearing Loss for Use in Communication Studies

In studying the problems of communication among coal miners, it was desirable to replicate electronically certain aspects of their hearing abilities so that one group of normal-hearing subjects could be used for the entire study. Tests were designed to determine the ability of miners to hear speech and nonspeech signals in noise and quiet, with and without ear protectors. Since miners cover a wide range of ages with varying amounts of hearing loss, the literature dealing with hearing of noise-exposed miners was surveyed and collated to obtain audiograms of three representative subgroups. From this threshold data, a linear transformation was used to obtain equal loudness contours for bands of noise. Three electrical filters were then developed from this data to approximate the frequency response aspects of the miners' hearing loss. The derivation of the filters and some results of tests involving their use will be described. [This research was supported by a contract with the U. S. Bureau of Mines.]

Equal loudness contours derived from sensory magnitude judgments.

Magnitude estimates were obtained for the loudness of 77 pure tones varying in frequency (11 values) and intensity (seven values) when (1) all 77 tones were presented intermixed within a session, and (2) all tones of one frequency were presented before presenting tones of another frequency. A power function described the growth of loudness for each frequency for both conditions 1 and 2, and the exponent of the power function varied with frequency. Equal loudness contours were derived from the power functions of Condition 1 and were compared to those obtained from other experiments using different procedures.

The audibility of low-frequency sounds

Contours of equal loudness and threshold of hearing under binaural free-field conditions for the frequency range 20–15 000 Hz were standardized internationally in 1961. This paper describes an extension of the data in the low-frequency range down to 3·15 Hz, at l levels from threshold to 70 phon. The latter corresponds to nearly 140 dB sound pressure level at the lowest frequency. Direct loudness comparisons were made between tones at intervals of an octave, and the resulting contours were checked by numerical loudness estimation.

An Improved Underwater Earphone

Am inproved underwater earphone, insensitive to depth, has been developed following the theoretical approaches reported earlier [B. B. Bauer and E. L. Torick, “Calibration and Analysis of Underwater Earphones by Loudness Balance Method,”J. Acoust. Soc. Amer. 39, 35–39 (1966)]. This new transducer offers good efficiency and yields speech reproduction comparable to most air acoustic earphones. The earphone design provides tympanic, rather than bone-conduction sensing, thereby providing directional signal information to the listener. Pairs of these devices have been used successfully in a directional communication system for underwater swimmers. Threshold levels and some man-earphone equal loudness contours were obtained for this device.

Pure-Tone Equal Loudness Contours for Standard Tones of Different Frequencies

Subjects (14 high-school students) made judgments of equal loudness by adjusting the intensity of comparison tones of ten different frequencies. The comparison tones were presented diotically alternately with standard tones (1-sec duration each). Each standard tone remained fixed at one frequency (125, 1000, or 8000 Hz) and one intensity (10, 20, 40, or 70 dB sensation level) while the data were collected for any single equal loudness contour. In this manner, families of equal loudness contours were generated for each of the three standard frequencies. The contours at 1000 Hz were compared with those for 1000 Hz in the literature. The contours for 125 and 8000 Hz, determined by otherwise using the same algorithm, were different in shape from the 1000-Hz set as well as from each other. These differences implied a violation of the transitivity assumption in the loudness calculating algorithm. Tests for transitivity among the three standard frequencies failed in many cases.

Loudness Level Summation for Octave Bands of Noise

During a previous investigation [“Researches in Loudness Measurement” IEEE Trans. Audio Electroacoust. AU-14, 141–151 (1966)] a new law of loudness level summation was established. This law may be formulated as follows: Loudness level L of a random noise, measured in octave bands, is L = Lm+20 log Σn (pn/pnm), where Lm is the loudness level of the loudest band, pn is the sound pressure of the nth band of the noise, and pnm is the sound pressure of the nth band of the Lmth equal loudness contour. It is shown that this law, which can readily be implemented in a loudness level meter, is in reasonably close agreement with loudness levels recomputed from Stevens' equation for loudness calculation [S. S. Stevens, “Procedure for Calculating Loudness,” J. Acoust. Soc. Amer. 33, 1577–1585 (1961)].

Calculation of the Perceived Level in PLdB

Modest improvements now appear possible in the procedure used for the calculation of loudness or noisiness. Young and Peterson [J. Acoust. Soc. Amer. 45, 834–838 (1969] have reexamined the precision of the two procedures, Mark VI loudness level and perceived noise level (PNL), which are both based on the same loudness summation rule [S. S. Stevens, J. Acoust. Soc. Amer. 28, 807–832 (1956)]. Mark VI predicted judgments of noisiness with slightly greater precision than PNL. That finding has led to a review of procedures for noise evaluation. Experiments with bands of noise over the past 25 years have provided some 24 contours of equal loudness, equal annoyance, equal acceptability, etc., from which a composite frequency-weighting function has been derived. This new weighting contour may replace the somewhat oversimplified loudness-index contour of Mark VI and the somewhat exaggerated contour used to calculate PNL in PNdB. The use of a common weighting contour for both loudness and noisiness suggests the possibility of a revised procedure (Mark VII) with which to calculate what may be called Perceived Level in PLdB.

On the relation between the acoustic reflex and loudness.

For each of four subjects, a set of equal-loudness contours constructed from obtained loudness balances was compared to contours of contra- or ipsilateral sinusoidal stimulations that activate the acoustic reflex to the same degree, as indicated by a constant change in acoustic impedance at the eardrum. Two subjects produced “normal” equal-loudness contours, showing close coincidence with the respective equal-reflex contours; the remaining two subjects produced “abnormal” equal-loudness contours, exhibiting significant departures from the respective equal-reflex contours. Results indicate no systematic difference in the sensitivity of the acoustic reflex to ipsi- and to contralateral stimulation. Middle-ear attenuations calculated from the magnitude of the acoustic impedance at the eardrum, together with estimates of the reflex-generated attenuations, were employed to transform the sound-pressure levels (SPL's) of the equal-reflex contours to relative values of volume velocity of the cochlear fluid. The transformed contours support the hypothesis that the acoustic reflex is activated to the same degree by sinusoidal stimulations producing the same total number of neural impulses within about 200 msec. For some subjects, equality of loudness between two sinusoidal stimulations appears to be attained under this same condition.

Impedance at the eardrum, middle-ear transmission, and equal loudness.

Acoustic impedance at the eardrum was measured on three subjects as a function of frequency (20 cps to about 1000 cps) and intensity (minimum 65 dB SPL; maximum 150 dB SPL, at eardrum) of a sustained ipsilateral sinusoidal stimulation by means of an inversely driven Zwislocki acoustic bridge. At lower intensity levels, acoustic impedance was independent of level, resistance and reactance varying with frequency according to R = af−1/2 and X = bf−3/4, respectively, from 20 cps to about 300 cps; above 300 cps, resistance remained essentially constant, and negative reactance decreased rapidly. At higher levels, one subject showed variations in impedance attributable to the acoustic reflex. At levels above 120 dB SPL, all subjects showed a rapid decrease of both impedance components at all frequencies. Middle-ear attenuations calculated from the magnitude of the acoustic impedance, together with previously obtained equal-loudness contours for the participating subjects, support the hypothesis that equality of loudness between two tones is attained when both generate the same total number of neural impulses within about 200 msec. The decrease in impedance at the highest levels is attributed to subharmonic radiation from the eardrum and/or a shift in the axis of rotation of the ossicles.

A loudness-level monitor for broadcasting

A Loudness Monitor for broadcasting has been developed by CBS Laboratories under joint sponsorship with the CBS Broadcast Group and is currently undergoing field tests. The Monitor uses the CBS Laboratories equal-loudness contours, the Loudness Level Summation Method described previously by Bauer and Torick, [7] and a revised ear ballistics characteristic. The steady-state calibration of the Monitor is in decibels re 1 mW into 600 Ω at 1000 Hz. The indications of the loudness level of program are in loudness level units (LU).

Matching functions and equal-sensation contours for loudness.

Loudness balances were collected from three subjects, employing 57 combinations of 13 frequencies extending from 20 to 5000 cps. Determinations were made from levels close to threshold to the highest levels tolerable by the subjects, with 5-dB intervals. Stimuli were applied by an earphone through individually moulded ear inserts, and were measured in decibels sound-pressure level a few millimeters from the eardrum. For each subject, a symmetric and transitive subset of the data was employed for constructing a set of matching functions and a set of equal-loudness contours. Matching functions generally were linear, or showed a double inflection (in log-log coordinates). Equal-loudness contours generally agree with previous determinations, but show a steeper rise towards low frequencies; below 300 cps, and at medium levels, the contours approach straight lines with a slope of −40 dB/decade. Obtained matching functions are compared to three sets of theoretical functions, favoring the matching functions derived from loudness theories developed by Zwicker and by Zwislocki.

Researches in loudness measurement

CBS Laboratories has performed a fundamental study of loudness from which several results already have emerged. A new set of equal-loudness contours has been obtained using octave bands of "pink" noise in a simulated living room environment. The CBS Laboratories contours differ radically from the Fletcher-Munson contours. Forward vs. backward inhibition tests were performed, from which a new summation function was deduced. A new duration vs. loudness level function was obtained for octave bands ranging in frequency from 125 Hz to 8 kHz. These data are being incorporated in an instrument for measuring sensory loudness level.

NEUROPHYSIOLOGICAL EVIDENCE FOR THE STEVENS POWER FUNCTION IN MAN.

Human evoked cortical responses to acoustic stimuli occurring within 150–170 msec after stimulus onset yielded input-output functions fairly comparable with Stevens' power functions from psychophysical experiments. The objective threshold and equal-loudness contours thus obtained were both in fair agreement with the well-known subjective measurements.

Pure-Tone Loudness Relations

A knowledge of pure tone loudness relations is of fundamental interest to all workers in the field of human hearing. Of these relations the pure tone equal-loudness contours, three sets of which have been independently established, are probably the best known. These three sets of contours have the same general shape but show considerable deviations over parts of the auditory diagram. Making use of the results obtained by different workers and assuming a recently established loudness-stimulus relation to hold at all frequencies in the audio range, a new set of equal loudness contours has been calculated. A set of curves giving the loudness of equal stimulus contours has also been calculated.

Procedure for Calculating Loudness: Mark VI

In order to improve the procedure for calculating the loudness of a complex sound, two changes have been made. (1) The equal loudness contours for bands of noise in a diffuse field have been approximated by straight lines in a log-log plot. (2) The spacing of the contours have been altered to reflect the nonlinear growth that takes place in the loudness level of bands of noise when their width exceeds the critical bandwidth. The basic formula for the addition of loudness across frequency remains the same: the total loudness St is given by St = Sm + F(Σ S − Sm), where Sm is the loudest band and F has the values 0.3, 0.2, and 0.15 for octave, half-octave, and third-octave bands. The revised procedure has the advantages that it can be described more easily and it agrees better with the available measurements on loudness level.

Calculation of Loudness: 1961 Revision

Steps have been taken to improve the procedure for calculating the loudness of a complex sound. Two changes have been made. (1) The equal loudness contours for bands of noise in a diffuse field [see Noise Control 3, 11–22 (1957)] have been approximated by straight lines in a log-log plot. (2) The spacing of the contours has been altered to reflect the nonlinear growth that takes place in the loudness level of bands of noise when their width exceeds the critical bandwidth. The basic formula for the addition of loudness across frequency remains the same: the total loudness St is given by St=Sm+F(ΣS−Sm), where Sm is the loudest band and F has the values of 0.3, 0.2, and 0.15 for octave, half-octave, and third-octave bands. The revised procedure has the advantages that it can be described more easily and it agrees better with the available measurements on loudness level.

New Sonic Methods for Arresting Attention

PROBABLY THE MOST commonly used audible signalling device is the electric bell or buzzer. Of the two types of bell demonstrated the smaller is the one used in the normal telephone set, while the larger is used as an extension bell where a louder ring is required. Figure I shows the principle of operation of the telephone bell. Movement of the armature, to which the striker is attached, is brought about by the interaction between the central permanent magnet and the electro-magnet produced by current flowing through the coils. The changing polarity of the electro-magnet (due to the alternating voltage applied to the coils) alternately attracts and repels each end of the armature, in which magnetism is induced by the permanent magnet. Although it is quite easy to produce an adequate sound from a telephone bell it is found on closer examination that it is inefficient in its conversion of electrical to sound energy. In order to determine the efficiency of an electro-acoustic transducer it is necessary to utilize the formula relating to electrical and acoustic power. These are summarized in Figure 2, which shows the similar nature of the two basic formulas. In the case of acoustic power, the relationship is shown between the power generated by a point source and the rate of flow of energy through unit area, or intensity (I) at a given distance from the sound source. The further relation between intensity and sound pressure enables acoustic power to be determined from a measurement of sound pressure, which is quite simply carried out by means of a sound level meter. Sound levels are measured in phons. The phon scale is logarithmic and takes into account the frequency response characteristic of the human ear. Figure 3, a set of equal loudness contours, shows that the sensation which a sound produces in the ear depends on the frequency of that sound. The loudness level of a tone in phons is numerically equal to the sound pressure level of a 1,000 cycles/second tone which sounds equally loud. This means, for instance, that for a sound at 100 cycles per second to have a loudness of zero phons it must have a sound pressure one

Threshold of Hearing of a Ring-Billed Gull

The threshold of hearing of a ring-billed gull was measured by the method of conditioned response. It varies with frequency in a manner quite similar to that of other birds. The minimum threshold occurs at about 2 kc and is about 28 db re 0.0002 microbar. The shape of the curve differs sufficiently from that of the irritation threshold so that the latter is probably not an equal loudness contour.