Outline. The ear and perception of sound (Psychoacoustics) A.1 Outer Ear Amplifies Sound. Introduction

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1 The ear and perception of sound (Psychoacoustics) 1 Outline A. Structure of the Ear B. Perception of Pitch C. Perception of Loudness D. Timbre (quality of sound) E. References Updated 01Aug0 Introduction 3 A. The Structure of the Ear 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

2 A.3 Inner Ear Senses Sound 7 B. Perception of Pitch 8 1. Range of Hearing. Pitch Discrimination and jnd 3. Combination tones Over 0,000 hair cells! Reference: 1a Range of Hearing 9 1b Test Hearing 10 High Frequency Test Low Frequency Test 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 186 Hertz 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%) 11 b. Beats Two tones closer than 15 Hertz we hear as a fused tone (average of frequencies) with a beat. 1 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 Demo:

3 3. Combination Tones 13 C. Perception of Loudness 1 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 171) 1. Fechner s law and decibel scale. Discrimination (jnd) 3. Threshold of hearing Demo: 1. Which sounds half as loud as first? Reference: b. 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 x bigger by the ear 16 Gustav Theodor Fechner ( ) 1c. Decibel Scale 17 a. JND: Just Noticeable Difference is 1dB Reference: 18 The decibel is a logarithmic scale db 10 Log Intensity 1 10 Watts m A multiplicative factor of 10x in intensity is +10 db 0 db is threshold of hearing 1 db is just noticeable difference 15 db is a whisper 60 db is talking 10 db is maximum safe level 150 db is jet engine (ear damage) 180 db stun grenade 10 ================== Power Ratio db ================== 3

4 b 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 19 c. Smaller than JND (7% change) Reference: 0 3a. Threshold of Hearing & Age (Presbycusis) 1 3b. 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 ) Example: you might be able to hear someone talking half a mile away under ideal circumstances Note Sound Pressure db (or SPLdB) is approximately half regular energy decibels (db). 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) D. Timbre 1. Waveforms and Timbre. Fourier Theory 3. Ohm s law of acoustics 3 1. Waveform Sounds Different shape of wave has different timbre quality Sine Wave (flute) Square (clarinet) Triangular (violin) Sawtooth (brass)

5 1b. Waveforms of Instruments 5 a. Fourier s Theorem 6 Helmholtz resonators (e.g. blowing on a bottle) make a sine wave As the reed of a Clarinet vibrates it open/closes the air pathway, so its either on or off, a square wave (aka digital ). Any periodic waveform can be constructed from harmonics. Bowing a violin makes a kink in the string, i.e. a triangular shape. Brass instruments have a sawtooth shape. Joseph Fourier b. FFT: Fast Fourier Transform 7 c. FFT of a Square Wave 8 A device which analyzes any (periodic) waveform shape, and immediately tells what harmonics are needed to make it Amplitude A Contains only odd harmonics n Sample output: tells you its mostly 10 k Hertz, with a bit of 0k, 30k, 0k, etc. Amplitude of n harmonic is: b n n A d. FFT of a Sawtooth Wave 9 e. FFT of a triangular Wave 30 Amplitude A Amplitude A Contains all harmonics n Contains ODD harmonics n Amplitude of n harmonic is: Amplitude of n harmonic is: b n n 1 A b n n A? 5

6 0 3a. Ohm s Law of Acoustics Ohm's acoustic law a musical sound is perceived by the ear as a set of a number of constituent pure harmonic tones, i.e. acts as a Fourier Analyzer 3b. Ohm s Acoustic Phase Law 3 Hermann von Helmholtz elaborated the law (1863?) into what is often today known as Ohm's acoustic law, by adding that the quality of a tone depends solely on the number and relative strength of its partial simple tones, and not on their relative phases Octave, in phase.0 Displacement Octave, phase shifted Displacement Phase (Degrees) Georg Simon Ohm ( ) Phase (Degrees) Hermann von Helmholtz ( ) For example:, the ear does not really hear the combined waveform (purple above), it hears both notes of the octave, the low and the high individually. The combined waveform here looks completely different, but the ear hears it as the same, because the only difference is that the higher note was shifted in phase. 3c. Ohm s Acoustic Phase Law 33 Hence Ohm s acoustic law favors the place theory of hearing over the telephone theory. Review: The telephone theory of hearing (Rutherford, 1886) would suggest that the ear is merely a microphone which transmits the total waveform to the brain where it is decoded. The place theory of hearing (Helmholtz 1863, Georg von Békésy s Nobel Prize): different pitches stimulate different hairs on the basilar membrane of the cochlea. E. Notes/References Fourier Applet (waveforms) Load Error on this page? FFT of waveforms: Demos: 3 6