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PHYS Week 5

by: Kait Brown

PHYS Week 5 PHYS 1270

Kait Brown

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Decibels, Sound Intensity Level, Logarithms
Science and Technology of Musical Sound
Cheryl Lawler
Class Notes
Decibels, Sound, Intensity, level, Logarithms
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This 6 page Class Notes was uploaded by Kait Brown on Sunday October 2, 2016. The Class Notes belongs to PHYS 1270 at University of North Texas taught by Cheryl Lawler in Fall 2016. Since its upload, it has received 4 views. For similar materials see Science and Technology of Musical Sound in Physics at University of North Texas.


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Date Created: 10/02/16
Unit Two Notes  The human ear is a highly sensitive sound receptor o Pressure fluctuations in the outer ear are transformed into vibrations of small bones (the ossicles) in the middle ear. o The ossicles are ultimately communicated to the cochlea in the inner ear o From there, the vibrations are further transformed by stereocilla (hair cells) into neural impulses distributed by frequency o Humans are capable of detecting pressure variations of less than 1 billionth of an -9 atmosphere (<10 atm)  Threshold of hearing o When the pressure is increases from threshold pressure by a factor of about I trillion (10 ), the sound becomes painful to the ear  Threshold of pain  This huge 10 dynamic range is converted into a logarithmic scale producing a more user-friendly scale. This allows users to clearly visualize huge changes in sound intensity.  Anatomy of the Ear o The structures of the outer and middle ear contribute to both the remarkable sensitivity and the wide dynamic range of human hearing o They can be considered to be both a pre-amplifier and a limiter for the human hearing process  Outer Ear  Gathers and focuses incoming sound on tympanic membrane  Amplifies frequencies important to human speech (2 kHz-5 kHz)  Convers pressure fluctuations to displacement o Pinna  “The Feather”  Matches ear canal to outside world  Collects more sound energy than the ear would receive without it o Meatus  “The Passageway”  Conducts sound into head o Tympanum  “The Drum”  Transforms pressure fluctuations into displacement  Middle Ear  The osccicles  “Little Bones”  Amplifies displacement  Protects against loud noise o Malleus  “The Hammer  Moved by Tympanum o Incus  “The Anvil”  Supported by ligaments that protect against loud percussion o Stapes  “The Stirrup”  Force multiplied by 1.3 because of lever action  Inner Ear  Converts displacement to neural impulses, sorted by frequency o Cochlea  “The Snail”  Converts displacement into neural impulses  Structure  Spiral Cone o Two ¾ turns o 3.2 cm long  Divided by Basilar Membrane  Waves enter on the top half  Waves exit on the bottom  Frequency Discrimination in Cochlea  20 Hz-20 kHz  Resonances in Basilar membrane and in HC cause spatial separation by frequency  Differential movement of membranes stimulate hair cells  Minimum stimulation for response.  Inhibition of neighbors causes non-linear response.  Average frequency range of te human voice is 120 Hz-1100 Hz. o Auditory Nerve  Neural impulses to brain  Stimulation in hair cells causes neuro-transmitters to stimulate neuron in auditory nerve. o Semicircular Canals  Detect motion and orientation  Organ of Corti  Hair Cells o Resolves about 1500 separate pitches with 16,000-20,000 hair cells o Sterecilla do not regenerate in mammals. o Is a neuron  Has threshold for stimulation  Neuron “fires”  Is either on or off  Firing neighbors inhibit neighbors  Support Cells  Auditory nerve fibers  How Does Anatomy Affect Perception?  Frequency response  Loudness perception  Phase insensitivity  Deafness o Disruption of “acoustic chain” o Nerve Death o Repeated acoustic traums can cause permanent and profound hearing loss or deafness  If you have experienced temporary hearing loss due to loud sounds you have had a warning. o Degrees of Hearing Loss  Mild hearing loss  Hearing sensitivity 25 dB-40 dB range  Difficulty hearing and understanding very soft sounds  Moderate hearing loss  Hearing sensitivity 40 dB-70 dB range  Difficulty hearing soft sounds and understanding conversation, especially in noisy environments.  Often don’t know what they are missing, like when they can’t hear someone’s name.  Severe hearing loss  Hearing sensitivity 70 dB-90 dB range  Cannot hear soft sounds, whispers, birds singing, or conversational level speech.  Profound hearing loss  Hearing sensitivity 90 dB and greater range  Often, people with profound hearing loss are referred to as deaf.  Those with profound hearing loss can typically only hear very loud environmental sounds.  For children, hearing loss compromises the proper development of speech and language unless appropriate amplification and intervention begin early. o Restore chain or increase amplitude o Large “non-linear” range of 12 orders of magnitude in intensity  Natural Response to Sound o Frequency  Where?  The location where the stereocilla are stimulated in the Cochlea. o Intensity  How much?  The number of hair cells that are stimulated by the sound determines the perceived loudness.  Power o P=E/t o Measure energy per unit time received by detector  Intensity o I=P/S=(E/t)/S  To remove dependence on size of detector (area, S), measure power per unit surface area (intensity, I) o I ɑ A 2  Intensity is the rate of energy flow and proportional to the square of the wave’s pressure amplitude, A o [W/m ] 2  The intensity of a sound wave (I) is the energy radiated per unit time per unit area o (I 1I 2=(A 1A )2 2  Comparing two sounds  Sound Intensity Level (SIL) o Is 10 times the logarithm of the ratio of the intensity of a sound and the threshold of hearing  Measured in decibel (dB) o Decibel Scale  A dB is 1 of a Bel 10  Named after Alexander Bell  Is a logarithmic scale based on the ratio of  The sound intensity threshold of hearing, 0  The actual sound intensity, I  SIL=10 log I/I0  Is a measure of loudness  For powers of 10 increases in the intensity of ratio, the loudness only goes up by ten. 10 log (x) X Sound Intensity Level in dB Ratio of I/0 Airplane 150 1,000,000,000,000,000 140 100,000,000,000,000 130 10,000,000,000,000 Pneumatic Drill, Threshold of Pain 120 1,000,000.000,000 Rock Concert 110 100,000,000,000 Stereo Music 100 10,000,000,000 90 1,000,000,000 80 100,000,000 70 10,000,000 Office 60 1,000,000 Home 50 100,000 40 10,000 30 1,000 Falling Leaves 20 100, 10 10 Threshold of Hearing 0 1 Frequencies and Descriptions of the Note “C” Frequency (Hz) Octave Description 16 to 32 1st The human threshold of feeling, and the lowest pedal notes of a pipe organ nd th 32 to 512 2 to 5 Rhythm frequencies, where the lower and upper bass notes lie 512 to 2048 6 to 7 th Defines human speech intelligibility, gives a horn-like or tinny quality 2048 to 8192 8 to 9 th Gives presence to speech, where labial and th fricative sounds lie 8192 to 16384 10 Brilliance, the sounds of bells and the ringing of cymbals. In speech, the sound of the letter “S” (8000-11000 Hz)  Just Noticeable Difference (JND) is the limen of difference that elicits 75% correct answers in a Two Alternative Forced-Choice test (2AFC test) o Why 75%?  In 2AFC  50% correct means random choice  100% means can always tell the difference  Thus, 75% is halfway between random and certainty Musical Dynamics Pianissimo pp Very soft 50 dB Piano P Soft 60 dB Mezzopiano mp Medium soft 66 dB Mezzoforte mf Medium loud 76 dB Forte F Loud 80 dB Fortissimo ff Very loud 90 dB Fortississimo fff Very, very loud 100 dB  The subjective measure of the magnitude of auditory sensation is called loudness o Measured in sone o In this system, one listens to two sounds and judges how much louder or softer a test sound is compared to the reference  A tone of 2 sone sounds twice as loud as a tone of 1 sone  Loudness of 1 sone defined by loudness of a 1000 Hz sine wave at 40 dB sound level o L ∝∛  An 8 singer ensemble sound about twice s loud as a soloist because ∛8=2  A choice of 64 sound about 4 times louder than a soloist because ∛64=4 o Since the loudness level for a given frequency can be approximated by a linear function of the Intensity Level  LL≈A (fIL-SIL threshold o One of the settings of a Sound Leve Meter (filter switch “A”) modifies the calibration of the instrument to account for the frequency dependence of human hearing  Sound Level is “dBA”


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