4. The Ear and the Perception of Sound (Psychoacoustics) 1 Outline A. Structure of the Ear B. Perception of Loudness C. Perception of Pitch D. References Updated May 13, 01 Introduction 3 A. The Structure of the Ear 4 Psychoacoustics is the study of subjective human perception of sounds. The length of the auditory canal has been greatly exaggerated A.1 Outer Ear Amplifies Sound 5 A. The Middle Ear The bones (ossicles) of the middle ear form a lever which amplifies the displacement by a factor of 3x. 6 The stirrup transfers the force to the much smaller area of the oval window, resulting in 10 to 30 x increase in pressure level Overall the sound is amplified by as much as 1000x or 30 db Auditory canal is a resonator at approximately 000 to 5000 Hertz. 1
A.3 Inner Ear Senses Sound 7 B. Perception of Loudness 8 1. Discrimination of Loudness. The Phon (Equal loudness) 3. The Sone & Perceived Loudness Over 0,000 hair cells! Reference: http://hyperphysics.phy-astr.gsu.edu/hbase/sound/place.html#c1 1a. JND: Just Noticeable Difference is 1dB Reference: http://www.phys.unsw.edu.au/jw/db.html 9 1b Discrimination of Loudness jnd = just noticeable difference 10 The ear s jnd for Loudness is approximately 1 db Or, sound must be 30% louder in intensity for us to just notice that it is louder. This depends somewhat on frequency (pitch) and loudness (intensity). We have trouble distinguishing changes in loudness for very the very loud or the very soft sounds 1c. Smaller than JND (7% change) Reference: http://www.phys.unsw.edu.au/jw/db.html 11 a. Threshold of Hearing & Age (Presbycusis) 1 Note Sound Pressure db (or SPLdB) is approximately half regular energy decibels (db).
a. Hearing Threshold The ear can hear as small as 10-1 Watts/m (one trillionth of a watt per square meter) ( 0.000,000,000,001 Watt/m ) 13 b Phon & Equal Loudness Level Hearing Threshold changes with frequency. The Phon scale is a frequency-adjusted decibel scale based upon perception. Hence 0 Phon is always the threshold, and 10 Phon sounds like its 10 db louder. 14 Example: you might be able to hear someone talking half a mile away under ideal circumstances Intensity is proportional to the square of the pressure amplitude Minimum ear can hear is 0.000,0 Pascals (Atmospheric pressure is 100,000 Pascal) The Fletcher-Munson curves are a way of mapping the db of a pure tone to the perceived loudness level in phons. c Steven s Phon 15 3a. Sone Scale (Steven s Power Law) 16 Ear is found NOT to exactly follow Fechner s logarithmic law (i.e. decibel scale). Stanley Smith Stevens (1906 1973) proposes Phon, which matches db at 1000 Hertz. 0 Phon is the threshold of hearing, which is adjusted for frequency (for example, at 100 Hertz, 0 Phon is equivalent to 35 db) Perception of loudness is also frequency dependent. 1000 Hertz: 10 db is perceived as 10 phon 100 Hertz: 10 db is perceived as 16 phon 1936 Stevens proposes the Sone scale is closer to perceived loudness ( Sones will sound to the ear as if it is twice as loud as 1 Sone) Phon = 40 +10Log ( Sone) A multiplicative factor of x in Sone corresponds to 10 Phon. 10 people singing will only appear to be x as loud as a soloist! 1/16 Sone is threshold of hearing 0.17 Sone is a whisper 4 Sone is talking 56 Sone is maximum safe level 048 Sone is jet engine (ear damage) =================== Phon Sone 0 0.065 10 0.15 0 0.5 30 0.5 40 1 50 60 4 70 8 80 16 90 3 =================== C. Perception of Pitch 1. Range of Hearing. Pitch Discrimination and jnd 3. Uncertainty Principle 17 1a Range of Hearing 18 Humans can hear from 16 to 0,000 Hertz (In terms of music, this is about 10 octaves) Piano only goes from 7.5 to 4186 Hertz 3
1b Test Hearing 19 1c. Test your Hearing 0 High Frequency Test http://audiocheck.net/audiotests_frequencycheckhigh.php Low Frequency Test http://audiocheck.net/audiotests_frequencychecklow.php http://www.phys.unsw.edu.au/jw/hearing.html a. Pitch Discrimination At 1000 Hz, the jnd is about 1 Hz (0.1%) At 0 Hz, the jnd is about 10 Hz (0.5%) 1 b. Beats Two tones closer than 15 Hertz we hear as a fused tone (average of frequencies) with a beat. Above 10,000 Hz, our discrimination is terrible. (Most music is in range of 30 to 0 Hertz) We can distinguish approximately 5000 different tones 401 403 410 40 440 450 480 Demo: http://www.phys.unsw.edu.au/jw/beats.html#sounds c. Combination Tones 3 3a. Pitch Uncertainty 4 When tones are far enough apart we hear them as two distinct tones We also hear difference and sum tones that are not really there (Tartini Tones 1714) The longer time you have T to measure a tone, the smaller your uncertainty in its frequency f Uncertainty Equation: f T 1 So to distinguish a and 401 Hertz tone you would need 1 second Demo: http://www.phys.unsw.edu.au/jw/beats.html#tartini http://www.phys.unsw.edu.au/jw/uncertainty.html 4
3b. Pitch & Amplitude 5 D. Notes/References 6 Tones above 000 Hz appear to increase in pitch with increase in db Tones below 000 Hz appear to decrease in pitch with increase in db At 0 Hz, increases 0 cents /30 db (14%) At 1000 Hz, decreases 10 cents/30 db (7%) http://en.wikipedia.org/wiki/phon http://en.wikipedia.org/wiki/sound_pressure_level http://en.wikipedia.org/wiki/weber-fechner_law http://en.wikipedia.org/wiki/stevens%7_power_law http://www.sfu.ca/sonic-studio/handbook/sone.html http://www.phys.unsw.edu.au/jw/dbnoflash.html http://www.phys.unsw.edu.au/jw/uncertainty.html http://www.phys.unsw.edu.au/jw/beats.html http://audiocheck.net/audiotests_frequencycheckhigh.php http://audiocheck.net/audiotests_frequencychecklow.php *An octave (doubling of frequency) is divided into 100 cents. The ear can discriminate a frequency difference of about 5 cents, so these effects are small! Demos: http://www.isvr.soton.ac.uk/spcg/tutorial/tutorial/tutorial_files/webhearing-shepard.htm 5