The ear and perception of sound (Psychoacoustics) General Physics Version Updated 2014July07 1

Outline A.Structure of the Ear B.Perception of Loudness (Energy) C.Perception of Pitch (Frequency) 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.Fechner’s law and decibel scale 2.Discrimination (jnd) 3.Threshold of hearing 8

1. Which sounds half as loud as first? Reference: 9

1b. Decibels: Fechner’s Law 1860 Fechner’s Law As stimuli are increased by multiplication, sensations increase by addition (Sensation grows as the logarithm of the stimulus) Example: A 10x bigger intensity sound is “heard” as only 2x bigger by the ear 10 Gustav Theodor Fechner ( )

1c. Decibel Scale The decibel is a logarithmic scale A multiplicative factor of 10x in intensity is +10 db 0 dbis threshold of hearing 1 dbis just noticeable difference 15 dbis a whisper 60 dbis talking 120 dbis maximum safe level 150 dbis jet engine (ear damage) 180 dbstun grenade 11 ================== Power RatiodB ___________________ ==================

2a. JND: Just Noticeable Difference is 1dB Reference: 12

2b 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 13

2c. Smaller than JND (7% change) Reference: 14

3a. Threshold of Hearing & Age (Presbycusis) Note “Sound Pressure dB” (or SPLdB) is approximately half regular “energy” decibels (dB). 15

3b. 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) 16

3c 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. 17 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.

3d 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 18

C. Perception of Pitch 1.Range of Hearing 2.Pitch Discrimination and jnd 3.Combination tones 19

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 20

1b Test Hearing High Frequency Test Low Frequency Test 21

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 22

2b. Beats Two tones closer than 15 Hertz we hear as a “fused” tone (average of frequencies) with a “beat”. 23 Demo:

3. 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) 24 Demo:

D. References & Online Demos Demos: b-hearing-Shepard.htmhttp:// b-hearing-Shepard.htm 25

D. Notes Excluded SONE scale of hearing 26