4. The Ear and the Perception of Sound (Psychoacoustics) Updated May 13,

Outline A.Structure of the Ear B.Perception of Loudness C.Perception of Pitch D.References 2

Introduction Psychoacoustics is the study of subjective human perception of sounds. 3

A. The Structure of the Ear The length of the auditory canal has been greatly exaggerated 4

A.1 Outer Ear Amplifies Sound Auditory canal is a resonator at approximately 2000 to 5000 Hertz. 5

A.2 The Middle Ear The bones (ossicles) of the middle ear form a lever which “amplifies” the displacement by a factor of 3x. 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 6

A.3 Inner Ear Senses Sound Reference: 7 Over 20,000 hair cells!

B. Perception of Loudness 1.Discrimination of Loudness 2.The Phon (Equal loudness) 3.The Sone & Perceived Loudness 8

1a. JND: Just Noticeable Difference is 1dB Reference: 9

1b Discrimination of Loudness jnd = “just noticeable difference” 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 10

1c. Smaller than JND (7% change) Reference: 11

2a. Threshold of Hearing & Age (Presbycusis) Note “Sound Pressure dB” (or SPLdB) is approximately half regular “energy” decibels (dB). 12

2a. Hearing Threshold The ear can hear as small as Watts/m 2 (one trillionth of a watt per square meter) ( 0.000,000,000,001 Watt/m 2 ) 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 0.000,02 Pascals (Atmospheric pressure is 100,000 Pascal) 13

2b Phon & Equal Loudness Level The Fletcher-Munson curves are a way of mapping the dB of a pure tone to the perceived loudness level in phons. 14 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.

2c Steven’s “Phon” 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 15

3a. Sone Scale (Steven’s Power Law) 1936 Stevens proposes the “Sone” scale is closer to perceived loudness (2 Sones will “sound” to the ear as if it is twice as loud as 1 Sone) A multiplicative factor of 2x in Sone corresponds to 10 Phon. 10 people singing will only appear to be 2x as loud as a soloist! 1/16 Soneis threshold of hearing 0.17 Soneis a whisper 4 Soneis talking 256 Soneis maximum safe level 2048 Soneis jet engine (ear damage) 16 =================== PhonSone ____________________ ===================

C. Perception of Pitch 1.Range of Hearing 2.Pitch Discrimination and jnd 3.Uncertainty Principle 17

1a Range of Hearing Humans can hear from 16 to 20,000 Hertz (In terms of music, this is about 10 octaves) Piano only goes from 27.5 to 4186 Hertz 18

1b Test Hearing High Frequency Test Low Frequency Test 19

1c. Test your Hearing 20

2a. Pitch Discrimination At 1000 Hz, the “jnd” is about 1 Hz (0.1%) At 4000 Hz, the “jnd” is about 10 Hz (0.25%) Above 10,000 Hz, our discrimination is terrible. (Most music is in range of 30 to 4000 Hertz) We can distinguish approximately 5000 different tones 21

2b. Beats Two tones closer than 15 Hertz we hear as a “fused” tone (average of frequencies) with a “beat”. 22 Demo:

2c. Combination Tones 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) 23 Demo:

3a. Pitch Uncertainty 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 400 and 401 Hertz tone you would need 1 second 24

3b. Pitch & Amplitude Tones above 2000 Hz appear to increase in pitch with increase in dB Tones below 2000 Hz appear to decrease in pitch with increase in dB At 4000 Hz, increases 20 cents /30 dB (14%) At 1000 Hz, decreases 10 cents/30 db (7%) 25 *An octave (doubling of frequency) is divided into 1200 cents. The ear can discriminate a frequency difference of about 5 cents, so these effects are small!

D. Notes/References Demos: hearing-Shepard.htmhttp:// hearing-Shepard.htm 26

Things to do Fechner’s law was done in previous topic. Part A: need more on number of hairs in ear, quantitative Part B: at what level do hairs break? Need a phon/sone table Upper range of hearing vs age Range of hearing from past classes Part C: critical bands?