Sound intensity

The intensity of sound is the power (energy per unit time) transmitted through an area of 1 m2 perpendicular to the direction in which the wave is travelling.

area

Intensity =

Power Area

- direction of -energy transfer

If sound from a point source moves at the same speed in all directions, the wave fronts form a series of expanding spheres. As the distance from the source increases, the area over which the energy is spread gets larger and the energy gets 'diluted'.

Sound waves from a point source

The wave fronts form concentric spheres with intensity i=P=.

The total power of the expanding wave front remains the same, so the intensity at a distance r1 from the source nxÀ

4pri

and the intensity at a distance r2 from the source

4p r2

The intensity falls off as —2 , where r is the distance from the r source.

When we double our distance from a source of sound, the intensity falls by a factor of 4.

this radio is twice as loud this soup tastes twice as good

I love you ten times more my toothache is twice as bad

r

"N

— nnnn

v

J

7.4.1 Real and perceived differences in the intensity of sound

Things that do not make sense

Any kind of perception is subjective and cannot be quantified directly. For example, nurses in hospital often ask patients to quantify the pain they feel on a scale of one to ten. Answers vary widely from patient to patient. Even for the same patient, the numbers must be taken purely as an indication. Suppose that one injection gives rise to a level 2 pain. Will two identical injections given together produce pain at level 4?

These four statements attempt to quantify a perception without defining units. The numbers are essentially random, 'I love you ten times more' could be replaced by 'I love you one hundred times more' without changing the meaning. The tests are not repeatable.

Things that do make sense

• You have turned up the radio so that I can just hear it.

• Salt has made this soup just about edible.

• I just about prefer Lisa to Jane.

• I think the aspirin is beginning to work.

These statements also quantify changes in perception, but this time a standard minimal step has been introduced as a unit.

For example, in the second statement we are comparing the taste of the soup with and without salt. The test could be repeated any number of times and the same result would be obtained. The change in perception is just noticeable. The size of the minimal step will depend very much on circumstances. A single candle will light up a dark room but will not be perceived in the bright midday sun. A cough which would disturb a solo violin recital would seldom be heard at a rock concert.

7.4.2 Quantifying perception

The concept of the just-noticeable difference was introduced by Ernst Weber (1795-1878). He set out to describe the relationship, for various human sense organs, between the physical magnitude of the stimulus and the perceived intensity of sensation. In one of his first experiments he increased, in very small steps, the weight held by a blindfolded person, in one hand and not the other, and recorded the steps of 'just-noticeable' difference.

Figure 7.9 illustrates such an experiment. The weightlifter is training with dumbbells of equal weight on each side. When the weights are light (top diagram) he notices that a small extra mass has been added to one side, but when he is lifting heavier weights (lower diagram) he does not notice the addition of the same small mass. The Weber-Fechner law deals with sensation and does not apply when he reaches the physical limit.

It is the perception of any sensation that is important to us because in the end we do not respond to differences in the stimuli themselves but to our perception of those differences.

Figure 7.9 Equal difference in weight but equal difference in perceived weight.

Weber observed that, for all senses, the smallest detectable change in sensation AS in a given stimulus is directly proportional to the existing intensity of the stimulus I:

Gustav Theodore Fechner (1801-1887) studied medicine under Weber. He suggested that the magnitude of a sensation S could be measured in terms of the number of just-perceptible steps above threshold required to attain it.

Integrating each side of Weber's equation,

Sensation is proportional to the logarithm of the stimulus.

7.4.3 Intensity level (loudness)

The term intensity level or loudness is sometimes used as a measure of the perception of sound. The ear is a remarkable organ, capable of detecting an enormous range of sound intensity. The Weber-Fechner law tells us how we perceive sounds, how loud they are.

Intensity level can be expressed in terms of a dimensionless unit called the decibel (dB).

The decibel is named after the Scot Alexander Graham Bell (1847-1922). Bell had a life-long interest in the education of deaf people and is generally credited with the invention of the telephone, which he patented in 1876. A recent US Congress resolution has however drawn attention to the contribution made by an Italian-American inventor, Antonio Meucci, who had demonstrated a rudimentary communications link in 1860, which had been described in New York's Italian language press.

Unable to afford a formal patent application for his lteletro-fono', Meucci filed a renewable one-year notice of an impending patent on 28th December 1871, but was not in a position to pay the $10 needed to maintain the caveat after 1874, and the patent was granted to Bell. Meucci took legal action and in January 1887, the US government initiated proceedings to annul the patent issued to Bell. The case was remanded for trial by the Supreme Court but the legal action terminated with the death of Meucci in 1889.

The role played by Meucci was formally recognized by the US Congress on 11th June 2002.

Resolved: 'That it is the sense of the House of Representatives that the life and achievements of Antonio Meucci should be recognized and that his work in the invention of the telephone

Alexander Graham Bell. Courtesy of An Post, Irish Post Office.

should be acknowledged.' Thomas Jefferson Papers, US library of Congress.

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