Chapter 4 : Sound Amplitude 

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We have learned that a disturbance causes pressures in the air particles surrounding the disturbance. Amplitude measures the sound pressure displacement above and below the equilibrium atmospheric level.

Remember that in normal conversation , a particle may be displaced only about one millionth of an inch. Sound pressure itself is very small. However , the dynamic range (range from the softest to the loudest sound) , is large. Our ears have a dynamic range in the millions. To measure the range, we must look into using logarithmic ratios. Just in case you have forgotten your math, let us review logarithms for a second. 

Logarithm n. Abbr. Log. The exponent indicating the power to which a fixed number, the base , must be raised to produce a given number. For example, if the logarithm of a , with n as the base, is x.   Then n^x = a.

In other words.

Using logarithms help abbreviate numbers that would take up whole pages if written out. For this reason it is easier to measure decibels (dB) in logarithm.

n. A unit used to express relative difference in power, usually between acoustic or electric signals, equal to 10 times the common logarithm of the two levels.

The power in a sound is measured in intensity, as it contacts an area like an eardrum , and is proportional to the square of the amplitude of the waveform. Intensity is expressed as power per unit area and measured in Watts (a unit of power equal to one joule per second) per square meter.

One bel (named after Alexander Graham Bell) is the ratio between two sounds whose intensities have a ratio of 10:1 , and a dec-ibel is one tenth of a bel. Therefore decibel is a unit for sound level differences between two sounds. In this case, a measurement relative to the threshold of hearing of 10^-12 Watts per square meter.

Decibel expresses a ratio. The absolute sound level coming out of a speaker is not important, so we can listen at any volume level. What we are looking for are changes in volume level compared to a standard reference signal. The amount of change is a ratio expressed in dB. A signal stronger than our reference creates a ratio that is + so many dB, while a signal weaker than the reference point creates a ratio that is - so many dB. The reference level is 0 . 0 is often used as a reference to our threshold of hearing.

In other words , in the following illustration , a 440 Hz sine wave peaks (peak value) at around 60 dB. 60 is the ratio to 0. When this sound wave hits the membrane of the ear, it pushes at +60 and then pulls at -60.

Some examples of intensity levels in density would be:

The lowest sound pressure level (SPL) that we can hear is equal to 0 spl (zero decibels sound pressure level) . The loudest level before discomfort is 120 db spl. 

If we measure an orchestra at its lowest amplitude, it may be 30 dB SPL, and the loudest amplitude may be 110 dB SPL. If we subtract the lowest and highest dB levels we find the dynamic range of the orchestra, 80 dB (110 dB - 30 dB = 80 dB).

Dynamic range in music is important, especially in the realm of digital audio recording.

For example: A noise gate can be used to block out low amplitude sounds that could ruin a recording, such as buzzes, hums, breathing, background noises and more. The noise gate accomplishes this by only allowing sounds to pass to the recording medium that are above a set dB threshold. The gate 'closes' if the amplitude drops below the set dB threshold.

Also, different gear responds a certain way to decibels. For instance, a recording mike may have a maximum SPL response of 130 dB, while a DAT recorder may have a dynamic range of >90 dB.

We interpret dB to be the loudness of an event. You have possibly heard the term 'pushing a lot of air' in reference to speakers at high volumes. The greater number of air particles displaced, the greater the pressure, the louder we perceive the disturbance to be.

For example. Place you hand in front of a speaker and gradually turn up the volume of some music. You can feel more air moving around the speaker as you crank it up. 

Ling Electronics of California makes a noise generator whose gigantic howl, loud enough to tear electronic equipment apart, is used to test the toughness of space-flight hardware. (1)

Scientific tests..reveal that changes in the circulation of the blood and in the action of the heart take place when a person is exposed to a certain intensity of noise. Even snatches of loud conversation are enough to affect the nervous system and thereby provoke constrictions in a large part of the blood circulation system...(2)

Professor Rudnick and his colleagues built the most powerful siren ever conceived to date. It made what was, as far as anybody knew, the loudest continuous sound ever heard on earth up to the time: 175 dB, some 10,000 times as strong as the ear-splitting din of a large pneumatic riveter. The frequency range of this enormous howl was from about 3,000 cycles per second to 34, 000 cps, in the ultrasonic range.

Strange things happened in this nightmarish sound field. If a man put his hand directly in the beam of a sound, he got a painful burn between the fingers. When the siren was aimed upwards, 3/4 inch marbles would float lazily above it at certain points in the harmonic field, held up and in by the field, Prof. Rudnick could make pennies dance on a silk screen with chorus-like perfection while balancing another penny on its edge. A cotton wad held in the field would burst into flame in about 6 seconds. " To satisfy a skeptical colleague", reports Prof. Rudnick, " we lit his pipe by exposing the open end of the bowl to the field" (1)

1) "The Sonic Boom", Max Gunther,  Playboy Magazine, May 1967.

2) "Noise and Health", Gunther Lehman,  The Unesco Courier, July 1967.