# Theory of Sound - An Overview

Discussion in 'General Instruction [BG]' started by Correlli, Dec 18, 2005.

1. ### Correlli

Apr 2, 2004
New Zealand
You know what they say - knowledge is power.

Source: Encarta

Theory of Sound
Sound is a physical phenomenon that stimulates the sense of hearing. Hearing takes place in humans when sound, aprox. between 20hz and 20Khz, reaches the inner ear. Hertz (Hz) is a unit of frequency equaling one cycle per second. Sound higher than 20Khz is called ultrasonic, sound lower the 20Hz is called subsonic. In general, waves can be propagated transversely or longitudinally. A sound wave is a longitudinal wave.

Physical Characteristics
A simple sound such as a musical pitch, can be describe as having three perceptual characteristics:
- Pitch
- Intensity (loudness)
- Quality (timbre)
These characteristics correspond to the three physical characteristics:
- Frequency -> Pitch
- Amplitude -> Intensity
- Harmonic Composition (wave form) -> Quality
Noise is a complex sound, a mixture of many different frequencies or notes not harmonically related.

Frequency
Frequency is perceived is being higher or lower sound. A sound source can produce the same frequency but have different qualities. Concert pitch A above middle C is 440hz. One octave above is 880hz, and two octaves below is 220hz and 110hz. Thus, by definition, an octave is the interval between any two notes the frequencies of which are in a 2/1 ratio.

A fundamental law of harmony states that two notes an octave apart, when sounded together, produce a consonant combination. A fifth and a major third produce successively less consonant (disonant) combinations. Physically, an interval of a fifth consists of two notes. These two notes have the frequencies of which bear the arithmetical ratio 3/2. The major third has a ratio 5/4 (Just Intonation). Frequency ratios of small whole numbers are said to be consonant. Frequency ratios that have larger whole numbers, are said to be dissonant. On a fixed-pitch instrument, such as a piano, it is not possible to arrange the notes so that all of these ratios hold exactly. In this situation tuning of Equal Temperment has been adopted.

Amplitude
Amplitude is the degree of motion of air molecules within the wave. Corresponds to the extent of rarefaction and compression that accompanies the wave. The greater the amplitude of the wave, the harder the molecules strike the ear drum and the louder the sound that is perceived. Can be expressed in terms of absolute units by measuring the actual distance of displacement of the air molecules. Sounds is generally expressed by comparing them to a standard sound, measured in decibels dB

Intensity
The distance at which a sound can be heard depends on its intensity. In a perfectly homogeneous medium (uniform in composition), a sound will be nine times as intense at a distance of 1 unit from its origin, as at a distance of 3 units. In the actual propagation of sound through the atmosphere, changes in the physical properties of the air, such as temperature, pressure, and humidity, produce damping and scattering of the directed sound waves.

Quality
If A (440 hz) above middle C is played on a violin, a piano, and a tuning fork, all at the same volume, the tones are identical in frequency and amplitude, but very different in quality. The tuning fork is regarded a the simplest tone of the three. Pure tones are seldom heard because of the properties of the ear. The violin and piano contain overtones, such as 880hz, 1320hz, and 1760hz. The exact intensity of these other components, which are called harmonics, determines the quality of the note.

Velocity of Sound
The frequency of a sound wave is a measure of the number of waves passing a given point in 1 second. The distance between two successive crests of the wave is called the wavelength. The wavelength of A (440hz) above middle C is about 78.2 cm (about 2.6 ft), and the wavelength of A below middle C is about 156.4 cm (about 5.1 ft).
Temperature:
- The speed of propagation of sound in dry air at a temperature of 0° C (32° F) is 331.6 m/sec (1088 ft/sec).
- When temperature increases, so does speed of sound.
Pressure:
- Sound travels slightly faster in moist air than in dry air, because moist air contains a greater number of lighter molecules.
Liquids and Solids:
- Sound generally moves much faster in liquids and solids, than in gases.
- Sound travels faster in warmer water.
- Sound is propagated very efficiently in steel.

Refraction, Reflection, and Interference
Sound moves forward in a straight line when traveling through a medium having uniform density.
Refraction - The turning or bending of wave when it passes from one medium (air temperature) into another of different density.
Reflection - An echo is the result of reflection of sound.
Diffraction and Interference - If sound from a single source reaches a listener by two different paths-one direct and the other reflected-the two sounds may reinforce one another; but if they are out of phase they may interfere, so that the resultant sound is actually less intense than the direct sound without reflection.

Sensations of Tone
If the ear of an average young person is tested by an audiometer, it will be found to be sensitive to all sounds from 15/20 Hz to 15,000/20,000 Hz. The ear is most sensitive in the range from A (440Hz) above middle C up to A four octaves higher (1760Hz). In this range a sound can be perceived hundreds of times fainter than a sound an octave higher above this range, or two octaves lower. Louder sounds at lower frequencies are felt more than heard. Notes of identical frequency but differing greatly in intensity may seem to differ slightly in pitch. At high intensities the ear is approximately equally sensitive to most frequencies, but at low intensities the ear is much more sensitive to the mid-high frequencies than to the lowest and highest. Sound-reproducing equipment that is functioning perfectly will seem to fail to reproduce the lowest and highest notes if the volume is decreased.

Three Important Types of Ordinary Sound
The three main types of sound include speech, music, and noise (water fall). Pure tones are seldom heard in the natural environment.
Music - A musical note contains, in addition to a fundamental frequency, higher tones that are harmonics of the fundamental frequency.
Speech - Speech contains a complex mixture of sounds, some (but not all) of which are in harmonic relation to one another.
Noise - Noise consists of a mixture of many different frequencies within a certain range.
The human ear has the ability to fill in harmonic gaps in a musical tone. Another imperfection of the ear in the presence of ordinary sounds is the inability to hear high-frequency notes when low-frequency sound of considerable intensity is present. This phenomenon is called masking.

2. ### Wrong RobotGuest

Apr 8, 2002
I'm more into wisdom myself. Knowledge is kinda meh.

3. ### Sippy

Aug 1, 2005
Stuart,Florida
I'll take anything I can get... Nice post!

4. ### SuperDuck

Sep 26, 2000
Wisconsin
There is some very cool info there! While it might not help a person musically, sometimes it's good for a bricklayer to know what his bricks are made out of.

The only thing I would comment on (and it's of relatively small importance) is that our hearing is most sensitive between about 1 kHz and 4 kHz, as opposed to the range listed above. It's kind of neat how it developed that way. Our speech patterns cover a wide range of frequencies, but those most critical for speech intelligibility fall into the range of 1 kHz to 4 kHz. Our hearing is specially tuned to those frequencies as a result.

The picture below is called a Fletcher-Munson curve. By following the line straight across from the left, you can see where the equivalent loundness at a given frequency is perceived by human ears. You might see that if flattens out a bit the louder the sound level. Our ears become more perceptive to low and high frequencies the louder the original content. That's why if you turn down your home theater to a low level as you answer the phone, the low-end seems to drop out.Here's a link that might explain a bit more eloquently than I am able to.