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Lecture

# Lecture 3

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University of Toronto Scarborough

Psychology

PSYC56H3

Mark Schmuckler

Fall

Description

PSYC56 Music Cognition
Lecture 3 Basic Dimensions of Sound
The Physics of Sound
All sounds are a result of a number of interesting and interacting processes. Sounds begin with the
vibration of an object.
Blowing through a mouth piece, expelling air through the vocal cords, pulling a string are all
examples of producing a sound.
The air vibrating within a tube or the vibrating string must transfer its sound energy to a medium,
some sound body. This sound body amplifies vibrations and transfers the vibrations to the air.
The air picks up these vibrations and the air moves vibrations, which is passed to our ear.
This is the process through which all sound occurs.
We can take any vibration and analyze vibration into component vibrations, each component
vibration moves independently.
Simple harmonic motion is caused by elastic restoring force, take some object and move it away from
its equilibrium, and then we let go of the object, there is a force that acts on that object o try and
bring it back to its resting point, equilibrium. The force that acts on that is proportional to the
distance that we moved that object from its resting point. The distance is called the displacement,
and this is how we produce most of the vibrating systems we are interested in.
Simple Harmonic Motion
The ball hits the equilibrium point, however it still has force, and goes past equilibrium amount, it
will overshoot by the exact same amount we compressed the string. Once it hits maximum
displacement on other side it shoots back past equilibrium point. This is the case if there is no friction
involved in the system.
We end up with a curve at the bottom of the diagram, called a sound wave.
The wave repeats itself indefinitely if there is no friction. This means we can look at the number of
times this wave repeats itself per some unit time. it will give us characterization of how fast this wave
is. This is called frequency. Unit time is the number of cycles that occur every second. The unit for
frequency is hertz.
The period is the time it takes to complete one cycle. The period is the inverse of the frequency.
The phase has to do with where that wave starts relative to resting position. The peak of the wave is
90 degrees, halfway back to resting position we are now at 180 degrees. When we get 2/3 of the way
to the maximum displacement in the opposite direction now at 270 degrees. When we get to resting
position after completing a circle now at 360 degrees or 0 degrees.
(b) Increasing the displacement (doubling it) of the string, the amplitude is going to be twice as much
as it was. We have the same weight and we actually have the same frequency, it is still going at the
same speed, and it still took the cycle the same time. We put more force, so we get more of a
displacement.
(c) Using a stiffer string, using the same displacement we used initially, there is an increase in
frequency. The stiffer spring has a faster frequency then the first, same displacement and same mass.
(d) A heavier string is going to make the string move slower, and there is a slower frequency.
The pitch of a musical note doesn’t change as it gets softer because the frequency stays the same.
Additivity and Superposition of Sine Waves
(a) Take two waves at identical frequencies. The amplitude of the resulting wave is adding the
amplitudes of both waves. (b) Take waves that differ in their frequencies, when we take a wave 90 degrees of out of phase, the
first wave starts at 0 and the other start at 90 (top of its displacement), the resulting wave is addition
of the two. We get a wave with the same frequency but differing amplitude.
(c) The dashed wave starts at 0 and dotted wave starts at 180. The two waves actually cancel each
other out resulting is a straight line.
(d) Take two waves of different frequencies, dotted wave is slightly faster frequency than dashed
wave. The resulting frequency is the lined wave. It is a much more complex wave. The important part
of this is that it is still a periodic wave, at some point that wave is going to repeat itself and it will be
cyclical as well.
(e) Take two waves of different frequencies. We can take sine waves and add them together and this
produces a new wave that may no longer be a sine wave but it is still a periodic wave, it still repeats
itself. This notion is interesting because it makes us wonder if we can reverse the process. Can we
take a complex wave form and can we break it down? We can do that.
Fourier Decomposition or Fourier Analysis
Fourier’s Theory demonstrates that we can take any repetitive complex wave and break it down into
a set of sine waves where these sine waves, all they are going to do, is differ in term of their
frequencies and their amplitudes and their phases.
The process of breaking the complex wave down is called Fourier Analysis
Fourier also discovered that the frequencies of the wave forms we are breaking them down into are
harmonically related.
The complex wave is just the sum of all the sine waves; it is the addition of the sine waves.
The sine waves are harmonically related, the frequencies lie in ratios to one another, they lie in a 2:1,
3:1, or whatever ratio. If the frequency of one wave was 200 hertz then the frequency of the next
wave would be 400 hertz, at a 2:1 ratio. *can there be a 1:1 ratio?
The first one is called the first harmonic, and the second is called the second harmonic. There are
three systems for labeling the harmonic. We call the first harmonic the fundamental harmonic
because it is the first harmonic we hear.
Take note that the 2 ndharmonic is also called the 1 overtone, and also the 2 ndpartial.
The square is called so because it looks like a square. A square wave is the sum of the odd number of
harmonics with amplitudes that are proportional to their number in the harmonic series.
rd
The 3 harmonic is 1/3 of the fundamental harmonic.
The 5 harmonic is 1/5 the amplitude of the fundamental harmonic.
Once we take the sum of the odd harmonic, it produced a square wave.
A saw tooth wave composes all the harmonics, odd and even.
The fundamental harmonic does not necessarily need to be the loudest. We do not hear all the
individual harmonics, but we hear the pitch, and it is normally the pitch of the fundamental
harmonic. It is possible to hear the upper harmonics above the fundamental harmonic.
th
In an English horn, the 5 harmonic is actually the loudest. In the square wave and saw tooth wave,
the first harmonic is the loudest, but looking at the last part of the diagram, in the English horn, the
th
5 harmonic is the loudest.
The Perception of Pitch
Physiology of the Ear
The c

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