The analogy between sound propagation through air and waves in water
was understood as early as Marcus Vitruvius Polio in the first century BC.
An interesting source of acoustic energy today is the loudspeaker: the cone of the loudspeaker vibrates in the air causing disturbances dependent on the electrical signals reaching the loudspeaker from the sound system. Effectively, the loudspeaker converts electrical energy into sound energy, which travels through the air as waves radiating from the loudspeaker:
Sound travels through the air at about 340 metres per second.
Intensity is a measure of the power in a sound, as it contacts an area such as the eardrum, and is directly proportional to the square of the amplitude of the waveform. Intensity is expressed as power per unit area and measured in Watts per square meter. The decibel scale is logarithmic and provides the most convenient physical measure of intensity. One bel (named after Alexander Graham Bell) is defined as the ratio between two sounds whose intensities have a ratio of 10:1, and a decibel (dB) is one tenth of a bel. Note that the Decibel is a unit for sound level differences between two sounds. In acoustics, dB is often used as an absolute measure of intensity - in this case, it is a measurement relative to the threshold of hearing of 10 (power -12) Watts per Sq. meter. Here are some sample intensity levels in decibels:
Threshold of hearing 0 Leaves rustling in the breeze 20 A quiet restaurant 50 Busy Traffic 70 Vacuum cleaner 80 Threshold of pain 120 Jet at takeoff 140
In the early nineteenth century, scientists started to attempt to measure the response of subjects to sounds with controlled physical characteristics. They determined that the perceptual attributes of loudness and pitch were strongly related to the physical variables of amplitude and frequency.
Only periodic (or nearly periodic) sounds have pitch: we cannot ascribe a pitch to noise. Sounds made by musical instruments, the human voice and tinkling wine glasses are regular and have pitch. Those that we describe as sounding higher have a higher pitch.
To a first approximation, pitch of a pure tone is proportional to the logarithm of frequency. This breaks down at very high or very low frequencies.
The piano below shows the relationship between the keys on a piano
keyboard, musical notation and frequency. As you can see, notes played
on a piano have frequencies between 27.5 Hz and 4,000 Hz.
(click to expand)
The notes of the piano are such that roughly equal increases of pitch are heard between any pair of adjacent keys. In terms of frequency, the ratio of frequencies between any two keys is constant (approximately 1.06). Therefore, the logarithmic scale for frequency matches up with the constantly spaced piano keys in this diagram.
In the case of complex tones, such as the sound of a bell, pitch may be ambiguous. In Psychoacoustic experiments, the pitch of a complex sound can be measured by asking a subject to adjust a sinusoid until its pitch matches that of the sound.
Loudness increases with the intensity of the sound
source, but is also influenced by the spectral content.
These equal loudness contours, developed by Fletcher and Munson in 1933,
have stood the test of time and appear in every book on psychoacoustics.
They show the uneven manner in which the auditory system responds to
tones of different frequencies:
(click to expand)
The ear is most sensitive to tones at frequencies between 200 and 5000 Hz, which is also the region of human speech sounds. At low frequencies, high intensities are needed to make a tone audible. The ear has extra sensitivity in the region of 2000 Hz to 4000 Hz, or around the resonant frequency of the auditory canal. As a matter of interest, this is the frequency region of both male and female screams.
The unit of loudness level is the phon, and is defined as the sound pressure level in dB of a 1000 Hz with the same subjective loudness.
Timbre is defined as that attribute of a sound that allows us to differentiate between two sounds of the same pitch, intensity and duration.
It used to be thought that timbre was related only to the relative strengths of the harmonics produced by an instrument, but recent research in computer synthesis of instruments has shown that the pattern of change over time of each of the components contributes to timbre. Instrument recognition is also dependent on the sounds that are associated with the "attack", for example the noise at the start of a trumpet sound, and to a lesser extent on the "release", as when a piano key is released.