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Human Hearing Time to read Chapter 6.1 and 6.2 of Berg & Stork
3.2 mm2 55 mm2
Uncoiled cochlea (schematic) limber stiffer http://www.howstuffworks.com/hearing1.htm
inner hair cell outer hair cell
An animation may help: http://www.maxanim.com/physiology/Cochlear%20Structures/Cochlear%20Structures.htm
Two frequencies f and 2f (one octave) 3.5 mm “same” interval corresponds to the same frequency ratio (fixed distance along the cochlea)
Weber-Fletcher Law feels like the same interval
overlap for frequencies differing by less than about 15% (minor third) sine wave excites about 1.2 mm of the basilar membrane
excited hair cells distance along the basilar membrane sharpening The amount of sharpening determined the just noticeable difference in frequencies
JND in pitch: 0.5% 2%
frequency up and down by 0.001 = 0.1% frequency up and down by 0.005 = 0.5%
Periodicity pitch and fundamental tracking (This is not Physics, it’s psychology) An overtone series like 2f, 3f, 4f, … which is missing the fundamental has a pitch equal to the f, 2f, 3f, 4f, … series (the brain “adds” the fundamental for the purpose of pitch determination 500 Hz + 750 Hz together, followed by the 250 Hz fundamental 900 Hz + 1200 Hz together, followed by the 300 Hz fundamental 700 Hz + 1050 Hz together, followed by the 350 Hz fundamental
500 Hz + 750 Hz has the same pitch as 250 Hz an octave above (x 2) BUT 750 Hz + 1000 Hz has the same pitch as 250 Hz an octave and a fifth above (x 3)
note D note D minus fundamental note D minus fundamental and 2nd harmonic
Aural harmonics sin(2p 50 t) sin(2p 50 t)+ 0.2 sin(2p 100 t) +0.1 sin(2p 150 t) +… extra frequencies “aural harmonics” 400Hz, 400Hz+802Hz, 400Hz+1202Hz
300Hz+400Hz, 300Hz+400Hz=700Hz, 702Hz, 300Hz+2 400Hz=1100Hz, 1102Hz rising fixed lowering
Sound localization How do we know where the sound is coming from ? • interaural level differences (ILD) • interaural time differences (ITD) • head-related transfer function (HRTF) http://www.aip.org/pt/nov99/locsound.html
Interaural level difference: one ear will be on the shadow cast by the head we can detect even 0.5 dB in ILD diffraction makes it ineffective at low frequencies
300 Hz: 2000 Hz:
Interaural time difference: peaks and through will arrive at ears at different times t ~ L/v ~ (0.15 m)/(340m/s) ~ 0.0005 s difference in arrival time distance between ears much shorter than synaptic delays !
Phase ambiguity: l/2=10 cm, f=340 m/s /0.2 m = 1700 Hz distance between ears
Artificial sounds and recording including ILD and ITD give a sense of localization but with the source inside the head
Head-related transfer function: includes the reflection, refraction and diffraction from ears, chest, head, …
Recordings using the hrtf give the sensation of a source outside the head
Aside: since we are talking about auditory illusions Tritone paradox: Are the tones going up or down ? What are they saying ?
Precedence effect The source appears to be entirely on the direction of the first (direct or reflected) sound to arrive sound appears to come entirely from the blue speaker