Transcript Slide 1
Human Hearing Time to read Chapter 6.1 and 6.2 of Berg & Stork 3.2 mm2 55 mm2 Ossicles Pretty small … Uncoiled cochlea (schematic) stiffer http://www.howstuffworks.com/hearing1.htm limber Cross section of cochlea Two theories for the vibrations inside the cochlea inner hair cell outer hair cell Loss of OHCs: incomplete deafness and hearing aids From cochlea to the brain An animation may help: http://www.maxanim.com/physiology/Cochlear%20Structures/Cochle ar%20Structures.htm length along basilar membrane 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 625Hz 1.25 500 Hz 781.25Hz 1.25 625Hz 976.56 Hz 1.25 781.25Hz feels like the same interval sine wave excites about 1.2 mm of the basilar membrane overlap for frequencies differing by less than about 15% (minor third) 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 an octave and a fifth above (x 3) 250 Hz 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 f n f1 m f 2 , n, m 0,1, 2,... 300Hz+400Hz, 300Hz+400Hz=700Hz, 702Hz, 300Hz+2 400Hz=1100Hz, 1102Hz f 2 f1 f 2 rising fixed lowering Shepard tones 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 This really should be heard on earphones but … 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