SOUND WAVES
The loudness of a sound correspond to the amplitude of the wave
pitch to frequency
tone quality of the mix of overtones
bank: frequency, compression, parallel, temperature, rarefaction
Sound
waves consist of zones of _____________ and ____________. The particles
are vibrating ____________ to the direction in which the wave travels. THe ____________ does not affect the speed of sound but air ____________ does:
Vair = 331 + 0.6 Tc (unit = m/s), Tc is the temperature in degrees Celsius
We express sound graphically as a wave
form, with the frequency corresponding to the compression and expansion of air
and the amplitude representing the volume. A pure wave (a sine wave)
produces a very flat sound. click here to see a sine wave and to listen to 440Hz pitch. Observe how the loudness of the sound affects the amplitude of the wave.
source: Berkeley College http://sheetmusic.berkeley.edu/courses/music23/andy/pagesandpics/
2) How fast will a wave travel in air at temperature of 15C ?
3)
Sound waves spread in 3 dimension. EAch crest is a sphere of
compression growing as it travels. Can you represent these wave fronts
in a diagram ? suppose the source is a tuning fork .
The
wave front area increases as the ________ of the radius (think area of
a sphere). The total energy is the same so the amplitude decreases
rapidly at greater distance from the source.
Unless the sound is trapped in a ____________________. (see optic2b.html)
4) With the temperature at 24C a tunning fork vibrates at 320Hz. What is the wavelength of the sound wave it produces ?
PITCH
5) The pitch of the sound is the frequency (the fundamental) of the wave. So a A-440 has a frequency of ______Hz
6)
An octave is the interval, for example, between middle C and high C. An
increase in pitch in any octave represents a doubling of the frequency of
the wave.
THe lowest note on a piano is an A with a frequency of 27.5Hz. What is the frequency of the A three octave higher ?
7) Notes sound harmonious together when their frequencies are in simple whole number ratios.
Using the table below, find the ratio of the frequency of the triad : C-E-G and F-A-C
| A | B | C | D | E | F | G | A |
| 440 | 495 | 528 | 594 | 660 | 704 | 792 | 880 |
OVERTONES
8)
A flute playing C sounds very different from a violin playing the same
note. The difference is the tone quality/ The note C specifies the
pitch. But the sound wave is made of many frequencies. THe lowest
frequency is called the fundamental and the fundamental specifies the
pitch. THe other are called overtones. EAch instrument produces its
characteristic mix of overtones and that is what gives each its special
character. A flute produces a nearly sine wave with few overtones,
especially in its upper register. A violin's voice haS many overtones.
In this example the fundamental is 440 Hz and the only overtone is 880 Hz.
When the sine waves are added together it will produce a 440Hz (same wavelength and frequency)
but the sound seems richer. see Berkeley College http://sheetmusic.berkeley.edu/courses/music23/andy/pagesandpics/
Here is another example. Not that the Sum is a wave with the same frequency then the 1st one but distorted. The resulting wave may be very
complicated, but can be broken down into basic units called "modes"
of oscillation, each of which is a sine wave:
Sound
spectra of a guitar. The pitch of this instrument is f1. We hear the frequency f1.
But the wave is made of many other frequencies called overtones (2f2,
3f2 ..). The distribution of the frequencies (which ones and the
amplitude) produced the tone of the instrument for this pitch. | 
Same guitar but pinched at a different place. THe pitch is the same. However, the
distribution of the frequencies (overtones) is not the same. Even
thought the pitch is the same, we hear a different tone.
source: Physic sof everyday phenomena, Mac Graw Hill |
Fill the blanks :
The
lowest frequency produces by an instrument is called the ___________.
Waves of higher frequencies are called _____________. A sound wave
consists of alternate compressions and ______________ spreading through
space. The speed of a sound wave in air depends only on _____________.
Overtones determine the _______ of a musical sound.
A Cello
plays low A at 110Hz. THe string is also producing waves at 220HZ, 330Hz,
440Hz, 550Hz. THe overtones are simple whole-number
multiples of its fundamental. That means the pitch is _________ even though the string produces other frequencies.
An open pipe resonates when the the length L is an integral number of half wavelengths,
L= λ1/2, L = 2 λ2/2, L = 3 λ3/2 , L= 4 λ3/2....
So λ1 = 2 L, λ2 = _____, λ3 = ____, λ4 = _____, λ5 = ____. Let's call the fundamental f1. f1= V/ λ1 = _____, f2 = _____, f3 = _____, f4 = _____ ...
Thus
the frequencies produced by an instrument with an open pipe with
fundamental frequency f1 are f1, f2 = ____ (first overtone) (use only f1 in the expression), ____ (second overtone),
_____ ( third overtone) , _____ (fourth overtone) , ____ ( ________).
REmember
1 octave higher = double the frequency. So the first overtone is one
________ higher than the fundamental. What is the ratio between f3 and
f2 ? In music a ratio in frequencies in 3:2 is called a fifth. So the
second overtone f3 is an _________ and a _______ above the fundamental.
But
drum 50HZ has overtones at: 79.7, 106.8, 114.8,145.9, 179.9... this is
noise because the overtones are not whole-number multiples of the
fundamental 50Hz. The pitch is still ____________.
.
9) An octave means: double he frequency. A fifth means a ratio of 3/2 between frequencies.
a fourth means a ration of 4/3. A third means 5/4. Fill the table then. Violin:
| Harmonic | Freq. Hz | Note | Comments |
| 1 | 131 | C3 | Fundamental f1 |
| 2 | 262 | C4 | 1 _____ Higher than f1 |
| 3 | 393 | G4 | A _______ above C4 |
| 4 | 524 | C5 | 2 ________ above fund.
and a fourth above G4 |
| 5 | 655 | E5 | A _______ above C5 |
| 6 | 786 | G5 | A _______ above C5
Harms. 4, 5 & 6 form a major chord |
9)
With the temperature at 22C, a violin plays middle C at 264Hz, what is
the wavelength of the second overtone of the sound wave produced in the
air ?
(for a violin, the overtones are multiples of the fundamental)
10) Fill the blanks: A drum produces no definite sense of pitch because its ______ do not form a series with integral ratios.
STANDING WAVES - RESONANCE
1)
When playing guitar the string will vibrate. The waves will move along
the string and will be reflected. Most of them will die. The ones that
stay producing a sound are called standing wave.
See below to see
the standing waves on a string. ANy pitch will be a combinaisons of
these standing waves called harmonics. (or overtones).
This picture shows the relationship between the length of the string and the wavelength of the wave.
harmonics in an organ pipe.
LOUDNESS - What we hear.
DIFFRACTION
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