8.1 Music and Musical Notes

1
8.1 Music and Musical Notes Its 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.
2

• Which of the following are musical and which are
  noise?

3
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.
4
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.
5
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.
6
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
7
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.
8
Increase length -gt decrease frequency Increase
tension -gt increase frequency Increase diameter
-gt decrease frequency Increase density -gt
decrease frequency
p. 283 1-5 Answer qualitatively!
9
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.
10
In its simplest, or fundamental mode of
vibration, the string vibrates in one segment.
This produces its lowest frequency, called the
fundamental frequency ( f0).
11
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
12
These vibrations are also referred to as
harmonics. Fundamental freq. fo First
harmonic First overtone f1 (2fo) Second
harmonic Second overtone f2 (3fo) Third
harmonic Third overtone f3 (4fo) Fourth
harmonic
13
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.
14
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.
15
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.
16
Resonance first occurs when the column is (1/4) ?
in length. The next possible lengths are 3/4 ?,
5/4 ?, etc. check wooden box with tuning fork
1st Resonant length
2nd Resonant Length
17
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 ¼ ? ¼ ? 16
cm ? 64cm (b) v f
? 512 Hz (64cm) 32 768 cm/s (327.7
m/s)
18
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 ?.
Resonance will next occur at lengths of ?, 3/2 ?,
2 ?, etc.test air tubes
1st Resonant Length
2nd Resonant Length
19
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 ? 3/2 ?
50 cm ? 0.33 m (b) f v/
? 300m/s / (0.33m) 9.0 x 102
Hz p. 290 1-7, p. 292 1-7, 9