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8.1 Music and Musical Notes
It’s important to realize the difference
between what is music and noise. Music is
sound that originates from a vibrating
source with one or more frequencies
(usually harmonious and pleasant). Noise
on the other hand is sound that originates
from a source with constantly changing
frequencies and is usually not ‘pleasant’ to
the ear. On an oscilloscope, noise would
not have a constant wave form or pattern.
Which of the following are musical and which
are noise?
There are three main characteristics of
musical sounds: pitch, loudness and
quality. Each of these characteristics
depends not only on the source of the
musical sound, but also on the listener.
Thus, they are called subjective
characteristics.
Pitch is the perception of the highness or
lowness of a sound; it depends primarily on
the frequency of the sound.
Loudness is the perception of the intensity
of sound.
Sound Quality is a property that depends on
the number and relative intensity of
harmonics that make up the sound.
In music, a pure tone is a sound where only
one frequency is heard. Musical sounds are
not normally pure tones; they usually
consist of more than one frequency. In
general, two or more sounds have
consonance if their frequencies are in a
simple ratio (simpler ratio produces more
consonance). Harmonious pairs of sounds
have high consonance; unpleasant pairs of
sounds have high dissonance, or low
consonance.
Unison is a set of sounds of the same
frequency. An octave has sounds with
double the frequency of the sounds in
another frequency. For example, a 200-Hz
sound is one octave above a 100-Hz sound.
The two common musical scales are the
scientific musical scale, based on 256 Hz,
and the musicians’ scale, based on 440 Hz.
p. 278
2
p. 280
3,4
p. 281 1-4
8.2 Vibrating Strings
Vibrating strings (examples?) are often used
to produce musical sounds. The frequency
of a vibrating string is determined by four
factors: length, tension, diameter, and
density. All of these factors are taken into
consideration when designing stringed
musical instruments, such as the piano,
guitar, cello, harp, lute, mandolin, banjo and
violin.
Increase length ->
decrease frequency
Increase tension ->
increase frequency
Increase diameter ->
decrease frequency
p. 283 1-5
Answer
qualitatively!
Increase density ->
decrease frequency
8.3 Modes of Vibration – Qualities of Sound
When a string, stretched between two fixed
points, is plucked a standing wave pattern is
produced. Nodes occur at both ends.
Different frequencies of varying amplitudes
may result depending on how many nodes
and antinodes are produced. The resulting
note is the sum of all of these different
vibrations of the string.
In its simplest, or fundamental mode of
vibration, the string vibrates in one segment.
This produces its lowest frequency, called
the fundamental frequency ( f0).
If the string vibrates in more than one
segment, the resulting modes of vibration
are called overtones. Since the string can
only vibrate in certain patterns (always with
nodes at each end) the frequencies of the
overtones are simple to determine.
1st overtone (f1)
f1 = 2fo
These vibrations are also referred to as
harmonics.
Fundamental freq.
First overtone
fo
f1 (2fo)
First harmonic
Second harmonic
Second overtone f2 (3fo)
Third harmonic
Third overtone
Fourth harmonic
f3 (4fo)
Stringed instruments vibrate in a complex
mixture of overtones superimposed on the
fundamental frequency. Very few vibrating
sources can produce a note free of
overtones. An exception is the tuning fork,
but even it has overtones when first struck.
However, because the overtones
disappear quickly, the tuning fork is
valuable in studying sound and tuning
musical instruments.
The quality of a musical note depends on
the number and relative intensity of the
overtones it produces along with the
fundamental frequency. The quality enables
us to distinguish between notes of the same
frequency and intensity coming from
different sources; for example, we can
easily distinguish between middle C on the
piano, on the violin, and in the human voice.
8.4 Resonance in Air Columns
Closed Air Columns
When a sound wave is sent down an air
column (closed at one end) the end of the
tube reflects the sound waves back.
Certain frequencies produce standing
wave patterns (through interference) that
amplify the original sound. The closed end
is fixed so a node is located there. The
open end of the column is free to vibrate
so an antinode is located there.
Resonance first occurs when the column
is (1/4) λ in length. The next possible
lengths are 3/4 λ, 5/4 λ, etc.
check wooden box with tuning fork
1st Resonant length
2nd Resonant Length
Sample Problem:
The first resonant length of a closed air
column occurs when the length is 16 cm.
(a) What is the wavelength of the sound?
(b) If the frequency of the source is 512 Hz,
what is the speed of sound?
(a) first resonant length
=¼λ
¼λ
= 16 cm
λ = 64cm
(b)
v
=fλ
= 512 Hz (64cm)
= 32 768 cm/s (327.7 m/s)
Open Air Columns
Resonance may also be produced in an
open air column(open at both ends).
Antinodes occur at free ends. This means
the first length at which resonance occurs
is 1/2 λ. Resonance will next occur at
lengths of λ, 3/2 λ, 2 λ, etc.
test air tubes
1st Resonant Length
2nd Resonant Length
Sample Problem:
The third resonant length of an open air
column occurs when the length is 50cm.
(a) What is the wavelength of the sound?
(b) If speed of the wave is 300 m/s, what is
the source frequency?
(a) third resonant length
= 3/2 λ
3/2 λ = 50 cm
λ = 0.33 m
(b)
f = v/ λ
= 300m/s / (0.33m)
= 9.0 x 102 Hz
p. 290 1-7, p. 292 1-7, 9