Rob van der Willigen ~robvdw/cnpa04/coll1/AudPerc_2007_P6

1. Auditory Perception Rob van der Willigen http://~robvdw/cnpa04/coll1/AudPerc_2007_P6.ppt

2. Today’s goal Understanding the perceptual scaling of sound intensity: LOUDNESS

3. Magnitude versus Loudness Magnitude estimation treats the perceiver as a measuring instrument capable of assigning numbers to sounds in proportion to their loudness. Equal loudness contours summarize the intensity levels that make tones of different frequencies sound equal in loudness.

4. Magnitude versus Loudness Loudnessis a subjective impression of the intensity of sound Loudness matchingis adjusting the loudness of one sound until it is equivalent to the loudness of another

5. Humans versus the rest

6. Psychoacoustics Physical Dimensions of Sound • Amplitude • - height of a cycle • - relates to loudness • Wavelength (λ) • - distance between peaks • Phase (j ) • - relative position of the peaks • Frequency (f ) • - cycles per second • - relates to pitch

7. Psychoacoustics Acoustic Units of Sound Measurement

8. Psychoacoustics Physical parameters of sound waves: Sound Intensity Sound Intensity (I) of a wave is the rate at which sound energy flows through a unit area (A) perpendicular to the direction of travel: Sound Pressure, P, is measured in watts [W=J/s] A is measured in square meters [m2]

9. Psychoacoustics Sound Intensity: The Decibel scale Sound Intensity Level: Intensity threshold of hearing I0 = 10-12 W/m2 Energy ratio Sound Pressure Level: Pressure threshold of hearing P0= 2 x 10-5 N/m2 = 20 mPa Pressure ratio

10. Psychoacoustics How does an acoustic sound level depend on distance from the source? • Intensity (and pressure) is inverse • proportional for free field propagation. • At a distance 2r from the source, the area enclosing the source is 4 times as large as the area at a distance r. • NB. The power radiated remains the same irrespective of the distance; consequently the intensity, the power per area, must decrease.

11. Psychoacoustics Sound Intensity: Inverse square law Sound intensity and the inverse square law • A doubling of distance from the sound source in the direct field will reduce the "sound level” by 6 dB. • That is, sound intensity level, I, decreases by 6 dB per doubling of distance from the source to 1/4 (25 %) of the sound intensity initial value. • This will reduce the sound intensity I (energy quantity) to 1/2² = 1/4 (25 %) and the sound pressure p (field quantity) to 1/2 (50 %) of the the initial value. I1 / I2 = r22 / r12

12. Psychoacoustics Sound Pressure: 1/r law • In acoustics, the sound pressure of a spherical wave front radiating from a point source decreases by 50% as the distance r is doubled, thus measured in dB it decreases by 6.02 dB. • The behavior is not inverse-square, but is inverse-proportional (blue-line). • Sound pressure decreases inversely as the distance increases with 1/r from the sound source. Sound pressure p and the inverse distance law 1/r

13. Psychoacoustics Inverse square law versus Inverse distance law The inverse square law 1/r2 shows the distance performance of energy quantities. This relates to sound intensity or density. The inverse distance law 1/r shows the distance performance of field quantities. This relates to sound pressure / particle velocity / particle displacement. Energy quantities are proportional to squared field quantities:

14. Psychoacoustics The Physical Relationship between Intensity (I) & Pressure (po) r is mass density or air 1.204 kg/m3 at 20o Celsius. n is speed or air, 343.2 m/s, p0 zero-to-peak pressure amplitude. z is acoustic impedance or air 413.2 kg/(s·m2) or 413.2 N·s/m3.

15. Psychoacoustics The Decibel scale Since sound measuring instruments respond to sound pressure the "decibel" is generally associated with sound pressure level. Sound pressure levels quantify in decibels the intensity of given sound sources. Sound pressure levels vary substantially with distance from source, and also diminish as a result of intervening obstacles and barriers, air absorption, wind and other factors. Sound Pressure Level (SPL): 20 × log(p/p0) = 10 × log(p/p0)², where  p0 = 2×10-5 N/m2. p = root mean square sound pressure  (N/m2) The usual reference level p0is 20×10-6 N/m2.

16. Psychoacoustics The Decibel scale • "Threshold of audibility'' or the minimum pressure fluctuation detected by the ear is less than 10-9 of atmospheric pressure or about  20×10-5 N/m2 (pascal) at 1000 Hz. • "Threshold of pain'' corresponds to a pressure 106 times greater, but still less than 1/1000 of atmospheric pressure.  • Because of the wide range, sound pressure measurements are made on a logarithmic scale (decibel scale). • Sound power levels are connected to the sound source and are independent of distance. Sound powers are indicated in decibel. • Lw = 10 × log (P / P0) where: P0 = reference power (W). • The usual reference level is 10-12 W, calculated from • p0 = 20 micropascal, which is the lowest sound persons of excellent hearing can discern. • Sound power is measured as the total sound power emitted by a source in all directions in watts (joules / second). Sound power levels do not vary with distance from source.

17. Psychoacoustics The Decibel scale NB. 1 Pa = 1 N/m2 ≡ 94 dB 1 bar = 105 Pa

18. Psychoacoustics The Decibel scale

19. Psychoacoustics The Decibel scale 0 dB = Threshold of Hearing ≡ TOH 10 dB = 10 times more intense than TOH 20 dB = 100 times more intense than TOH 30 dB = 1000 times more intense than TOH An increase in 10 dB means that the intensity of the sound increases by a factor of 10 If a sound is 10x times more intense than another, then it has a sound level that is 10 times x more decibels than the less intense sound An increase of 6 dB represents a doubling of the sound pressure An increase of about 10 dB is required before the sound subjectively appears to be twice as loud. The smallest change of the pressure level we can hear isabout 3 dB

20. Psychoacoustics Counting Decibels Sound Intensity level of super imposed sources: where L1, L2, …, Ln are SIL [dB]

21. Psychoacoustics Sound Density When dealing with noises, it is advantageous to use density instead of sound intensity e.g., the sound intensity within a bandwidth of 1 Hz. The logarithmic correlate of the density of sound intensity is called sound intensity density level, usually shortened to density level, LE. For white noise, l and SIL are related by the equations given above where Δf represents bandwidth of the sound.

22. Psychoacoustics Physical parameters of sound waves: Noise Density sound intensity density level sound energy density

23. Psychoacoustics Physical parameters of sound waves: Power Spectrum Density The Intensity Density Level of three types of NOISES: WHITHE NOISE BROWN (RED) NOISE GRAY NOISE Intensity density level [dB] Log Frequency [Hz]

24. Psychoacoustics Physical parameters of sound waves: Power Spectrum Density Power Spectral Density (PSD) is the frequency response of a random or periodic signal. PSD shows the strength of the variations per unit frequency as a function of frequency. The PSD is the average of the Fourier transform magnitude squared, over a large time interval. It tells us how the average intensity is distributed as a function of frequency. Plot shows de PSD of white Noise

25. Psychoacoustics THE BELL DECODER

26. Psychoacoustics Auditory sensitivity: Absolute thresholds MAF Minimum Audible Field thresholds MAP Minimum Audible Pressure thresholds SPL at listener’s tympanic membrane sound presented over headphones (monaural) SPL estimated from the sound level in a test coupler attached to earphone. Differences in the two measures are due to some binaural advantage, outer-ear filtering (mid frequencies), and physiological noise (low frequencies). sound pressure level for pure tone at absolute threshold in a free field tested in a room, using loudspeakers, listening binaurally, 1 meter from source SPL calibrated using microphone, with listener not present.

27. Psychoacoustics Auditory sensitivity: Absolute thresholds Differences in the two measures are due to some binaural advantage, outer-ear filtering (mid frequencies), and physiological noise (low frequencies).

28. Psychoacoustics Auditory sensitivity: Hearing range (MAF)

29. Psychoacoustics Auditory sensitivity: upper limit

30. Psychoacoustics Auditory sensitivity: Absolute thresholds Hearing Level (dB HL) Threshold of hearing, relative to the average of the normal population. For example, the average threshold at 1 kHz is about 4 dB SPL. Therefore, someone with a threshold at 1 kHz of 24 dB SPL has a hearing level of 24 - 4 = 20 dB HL. Audiograms Audiograms measure thresholds in dB HL, and are plotted “upside-down”. Measurements usually made at octave frequencies from 250 Hz to 8000 Hz. Threshold microstructure Individuals show peaks and dips as large as 10 dB over very small frequency differences (probably due to OHCs and “cochlear amplifier”).

31. Psychoacoustics Auditory sensitivity: Audiometric curve (audiogram) Plot A shows the threshold of hearing or audibility curve for a patient with a hearing loss (curve b) and a normal curve (curve a). Notice that the patient's threshold is higher for every frequency above 128 Hz. The normal audibility curve is usually converted to a straight line at 0 dB loss, and the patient's values are plotted as deviations from the normal values. The result is a hearing loss curve b, as shown in plot B.

32. Psychoacoustics Auditory sensitivity: Audiometric curve (hearing loss)

33. Psychoacoustics Auditory sensitivity: Audiometric curve (hearing loss) Conduction lossstems from damage to outer or middle ear (areas involved in conduction of sound energy to the inner ear). Sensory/neural lossis associated with damage to the inner ear or auditory cortex.

34. Psychoacoustics Auditory sensitivity: Audiometric curve (hearing loss) Blue lines in the audiogram indicate the hearing loss as measured by air conduction, whereas pink lines indicate the hearing loss as measured by bone conduction. Typically, in neural hearing loss (A), both measures show the same pattern of loss. Surgery is not indicated for this form of hearing loss because the neural tissue probably cannot be repaired, but some improvement in hearing is possible with a hearing aid, depending upon the nature of the damage. The audiogram of a person with pure conduction hearing loss (B). Here, bone conduction (pink) is near normal, i.e., near 0 dB loss, but air conduction is impaired (blue). Notice that the air audiogram is nearly flat with conduction hearing loss (B, pink), but there is a differential loss, depending upon frequency, in nerve hearing loss (B, blue).

35. Psychoacoustics Absolute thresholds: temporal integration Audiometric thresholds and international threshold standards are measured using long-duration tones (> 500 ms). Detectability of tones with a fixed level decreases with decreasing duration, below 300 ms. IL is the minimum intensity which is an effective long duration stimulus for the ear. trepresents the integration time of the auditory system. Thus, the auditory system does not simply integrate stimulus time (Intensity x duration) It may also vary with frequency.

36. Psychoacoustics Absolute thresholds: temporal integration The absolute threshold for detecting sounds is affected by duration Up to a few hundred milliseconds the threshold for detecting sounds decreases (more sensitive) with increasing duration Effect of duration on loudness causes variability in the results For a given intensity, loudness increases with duration up to 100-200ms

37. Psychoacoustics Perceived Loudness: Equal-loudness Contours The pressure, or intensity, of a sound wave is not solely responsible for its loudness – frequency is also important. 1 kHz is used as a reference. By definition, a 1-kHz tone at a Intensity level of 40 dB SPL has a loudness level of 40 phons. Any sound having the same loudness (no matter what its SPL) also has a loudness level of 40 phons. Equal-loudness contours are produced using loudness matching experiments (method of adjustment or method of constant stimuli). Equal-loudness contours

38. Psychoacoustics SPL is not a measure of Perceived Loudness • Loudness is defined as • the attribute of auditory sensation in terms of which sounds can be ordered on a scale extending from quiet to loud. • Two sounds with the same sound pressure level may not have the same (perceived) loudness • A difference of 6 dB between two sounds does not equal a 2x increase in loudness • Loudness of a broad-band sound is usually greater than that of a narrow-band sound with the same (physical) power (energy content)

39. Psychoacoustics Perceived Loudness: Equal-loudness Contours The pressure, or intensity, of a sound wave is not directly related to its loudness – frequency is also important.

40. Psychoacoustics Perceived Loudness: phone • A unit of LOUDNESS LEVEL (L) of a given sound or noise can only be • derived from indirect loudness measurements • (see e.g., the Fletcher and Munson experiment) • If SPL at reference frequency of 1kHz is X dB – the corresponding equal • loudness contour is X phon line. • Phon units can’t be added, subtracted, • divided or multiplied. • 60 phons is not 3 times louder than 20 phons! • The sensitivity to different frequencies is more • pronounced at lower sound levels than at higher. • For example: a 50 Hz tone must be 15 dB higher • than a 1 kHz tone at a level of 70 dB

41. Psychoacoustics Perceived Loudness: sound level meters The shapes of equal-loudness contours have been used to design sound level meters (audiometer). At low sound levels, low-frequency components contribute little to the total loudness of a complex sound. Thus an A weighting is used to reduces the contribution of low- frequencies.

42. Psychoacoustics Perceived Loudness: A-weighting & sound level meters A-weighting is only really valid for relatively quiet sounds and for pure tones as it is based on the 40-phon Fletcher-Munson curves which represented an early determination of the equal-loudness contour for human hearing. Nevertheless, A-weighting would be a better match to the loudness curve if it fell much more steeply above 10 kHz, and it is likely that this compromise came about because steep filters were difficult to construct in the early days of electronics. Nowadays, no such limitation need exist. If A-weighting is used without further band-limiting it is possible to obtain different readings on different instruments when ultrasonic, or near ultrasonic noise is present. Accurate measurements therefore require a 20 kHz low-pass filter to be combined with the A-weighting curve in modern instruments. This is defined in IEC 61672 as A-U weighting and while very desirable, is rarely fitted to commercial sound level meters.

43. Psychoacoustics Perceived Loudness: Masking Auditory masking occurs when background noise makes sound inaudible. Broadband noise is contains energy at all audible frequencies. Bandpass noise removes energy from the low- and high-frequency ends of the spectrum.

44. Psychoacoustics Loudness Scaling: Magnitude of perceptual change Fechner assumed that a JND for a faint reference sound produces the same difference in sensation as does the JND for a loud reference. As it turned out, this assumption is not valid, as shown by Stevens (1957) he simply asked subject to asses supra-threshold stimuli. Measure of loudness: sensation intensity (S) in JND units

45. Psychoacoustics Louness Scaling: Stevens’ Power law Another function relating Loudness S in sones to stimulus intensity in I: The exponent m describes whether sensation is an expansive or compressive function of stimulus intensity. The coefficient a simply adjusts for the size of the unit of measurement for stimulus intensity threshold above the 1-unit stimulus. =0.3

46. Psychoacoustics Auditory sensitivity: JND Smallest detectable change in sound level equals 0.3-2dB for a wide range of levels and types of sound A value of 0.5-1dB for wideband noise – holds from about 20dB to 100dB above threshold – JND increases for sounds close to absolute threshold For pure tones the JND for loudness varies slightly with frequency (best 1-4 kHz) and may improve at higher sound levels

47. Psychoacoustics Loudness Scaling

48. Psychoacoustics Loudness Scaling: sone vs. phon SONE: a unit to describe the comparative loudness between two or more sounds. One SONE has been fixed at 40 phons at any frequency (40 phon curve). 2 sones describes sound two times LOUDER than 1 sone sound. A difference of 10 phons is sufficient to produce the impression of doubling loudness, so 2 sones are 50 phons. 4 sones are twice as loud again, viz. 60 phons. p is the base pressure of a sinusoidal stimulus, po is its absolute threshold.

49. Psychoacoustics Predicting Loudness Currently, predictors of loudness are only successfully for sound stimuli extending over many seconds. Note that the dBA scale does not include bandwidth influences on loudness (etc.). It is better than the dB SPL scale, but far away from human perception

50. Psychoacoustics Neural Coding of Loudness Neural Coding related to the perception of loudness: Increase in sound level: increased BM movement leads to increased firing rates in the neurons of the auditory nerve spread of activity to adjacent neurons the summation of neural activity across different frequency channels – critical bands