Transcript musical sound

MUSICAL ACOUSTICS
HEARING
Science of Sound
Chapter 5
Further reading: “Physiological Acoustics” Chap. 12 in Springer
Handbook of Acoustics, ed. T. Rossing (2007)
“Effect of Noise on People” Chap. 31 in Science of Sound.
MUSICAL ACOUSTICS
The human ear is a remarkably sensitive (and delicate)
organ. It responds over an intensity range of more
than 1012 (1,000,000,000,000) and a frequency range
of nearly 1000 (or more than 9 octaves)!
The human ear is a remarkably sensitive (and delicate)
organ. It responds over an intensity range of more
than 1012 (1,000,000,000,000) and a frequency range
of nearly 1000 (or more than 9 octaves)!
Human vision is remarkable, too, but the frequency
range doesn’t begin to compare with that of human
hearing. The frequency range of vision is about one
octave (4x1014 to 7x1014 Hz).
RANGE OF HEARING
STRUCTURE OF THE EAR
Outer, middle and inner ear
THE EAR
MIDDLE EAR:
THE OSSICLES
EAR FUNCTION
THE COCHLEA
ORGAN OF CORTI
Resting on the basilar membrane is the delicate organ
of Corti, a gelatinous mass about 1 ½ inch long. This
“seat of hearing” has several rows of tiny hair cells, to
which are attached nerve fibers.
OUTER AND INNER HAIR CELLS
RESTING ON THE BASILAR MEMBRANE IS THE DELICATE ORGAN OF
CORTI, WHICH INCLUDES SEVERAL ROWS OF TINY HAIR CELLS TO
WHICH ARE ATTCHED NERVE FIBERS: ABOUT 4000 INNER HAIR CELLS
IN A SINGLE ROW AND ABOUT 12,000 OUTER HAIR CELLS IN SEVERAL
ROWS.
EACH HAIR CELL HAS MANY HAIRS OR STEREOCILIA. BENDING OF
THE STEREOCILIA STIMULATES THE HAIR CELLS, WHICH IN TURN
EXCITE NEURONS IN THE AUDITORY NERVE.
OUTER AND INNER HAIR CELLS
RESTING ON THE BASILAR MEMBRANE IS THE DELICATE ORGAN OF
CORTI, WHICH INCLUDES SEVERAL ROWS OF TINY HAIR CELLS TO
WHICH ARE ATTCHED NERVE FIBERS: ABOUT 4000 INNER HAIR CELLS
IN A SINGLE ROW AND ABOUT 12,000 OUTER HAIR CELLS IN SEVERAL
ROWS.
EACH HAIR CELL HAS MANY HAIRS OR STEREOCILIA. BENDING OF
THE STEREOCILIA STIMULATES THE HAIR CELLS, WHICH IN TURN
EXCITE NEURONS IN THE AUDITORY NERVE.
INNER HAIR CELLS TRANSMIT SIGNALS TO THE AUDITORY NERVE
FIBERS
OUTER AND INNER HAIR CELLS
RESTING ON THE BASILAR MEMBRANE IS THE DELICATE ORGAN OF
CORTI, WHICH INCLUDES SEVERAL ROWS OF TINY HAIR CELLS TO
WHICH ARE ATTCHED NERVE FIBERS: ABOUT 4000 INNER HAIR CELLS
IN A SINGLE ROW AND ABOUT 12,000 OUTER HAIR CELLS IN SEVERAL
ROWS.
EACH HAIR CELL HAS MANY HAIRS OR STEREOCILIA. BENDING OF
THE STEREOCILIA STIMULATES THE HAIR CELLS, WHICH IN TURN
EXCITE NEURONS IN THE AUDITORY NERVE.
INNER HAIR CELLS TRANSMIT SIGNALS TO THE AUDITORY NERVE
FIBERS
OUTER HAIR CELLS ACT AS BIOLOGICAL AMPLIFIERS. WHEN THEIR
STEREOCILIA ARE BENT, THE CELL CHANGES ITS LENGTH AND
PUSHES AGAINST THE TECTORIAL MEMBRANE, AMPLIFYING THE
SOUND. OUTER HAIR CELLS ADD ABOUT 40 dB OF AMPLIFICATION.
In addition to the air conduction, sound can reach the
inner ear by bone conduction. The principle of bone
conduction is used in some hearing aids and other
listening devices.
Sing “aa-oo” with fingers stopping your ears.
In addition to the air conduction, sound can reach the
inner ear by bone conduction. The principle of bone
conduction is used in some hearing aids and other
listening devices.
The vibrations in compressional bone conduction are
created by stimulation of sensory cells by high-frequency
sounds as they compress the bony case around the inner
ear.
Inertial bone conduction involves the vibration of the
entire skull as it reacts to low-frequency sound waves
Bone conduction is one reason why a person’s voice
sounds different to him/her when it is recorded and
played back (or on the telephone).
Because the skull conducts lower frequencies better
than air, people perceive their own voices to be lower
and fuller than others do, and a recording of one’s own
voice frequently sounds higher than one expects it to
sound.
RESPONSE OF THE BASILAR MEMBRANE
TO A PAIR OF TONES
AS THE INTERVAL DECREASES THEIR RESPONSE
CURVES SHOW INCREASING OVERLAP
CRITICAL BANDWIDTH
CONSTANT AT LOW
FREQUENCY BUT
PROPORTIONAL TO f
AT HIGH FREQUENCY
SOUND SOURCE LOCALIZATION
PRECEDENCE EFFECT
(Also called “Haas effect” or “Law of the first wave front”)
THE SOURCE IS PERCEIVED TO BE IN THE
DIRECTION FROM WHICH THE FIRST SOUND
ARRIVES, PROVIDED THAT:
1. Successive sounds arrive within ~ 35 ms;
2. Successive sounds have spectra and time envelopes
similar to the first sound;
3. Successive sounds are not too much louder than the
first sound.
LOGARITHMS
Logarithms are so important in understanding sound and
music that it is worthwhile to take time to review or
introduce them.
The logarithm to the base 10 of a number x is the power
to which 10 must be raised to equal x.
For example, 100=102 so the logarithm of 100 (to base 10)
is 2 (log 100 = 2).
LINEAR
LOGARITHMIC
LOGARITHMS
AND POWERS
OF TEN
PRACTICE PROBLEMS (no calculator, please)
2.1x102 +1.4x10-2 =
3.0x108/300 =
log 8 =
log 2x107 =
log ½ =
log 1/5 =
log 200 =
log 400 =
log 500 =
SOLUTIONS TO PRACTICE PROBLEMS
2.1x102 +1.4x10-2 = 210 + 0.014 = 210.014
3.0x108/300 = 106
log 8 = log 23 = 3 log 2 = 0.903
log 2x107 = log 2 + log 107 = 7.301
log ½ = -log 2 = -0.301
log 1/5 = log 2/10 = 0.301-1 = -0.699
log 200 = log 2 + log 100 = 2.301
log 400 = log 2 + log 2 + log 100 = 2. 602
log 500 = log 1000 – log 2 = 3 – 0.301 = 2.699
DEPENDENCE OF SUBJECTIVE QUALITIES
OF SOUND ON PHYSICAL PARAMETERS
ASSIGNMENT FOR MONDAY, JAN. 25
Exercises 1-9 (p. 97-98)
Read chapter 6 Sound Pressure, Power, and Loudness
Plot hearing curve using the UNSW website (do it twice)