Intensity and Loudness

Author: N.H. Crowhurst

As well as having different frequencies, sounds also differ in loudness. This means that the vibrations we hear are of greater or smaller intensity. The horn of an ocean liner produces such an intense vibration that you can feel it as well as hear it. A piece of paper held near the source of such a sound will vibrate hard enough to numb your fingers.

Vibrations that can be felt (piece of paper picks up sound)

The ticking of a watch, however, is of very low intensity. Unless the surroundings are fairly "quiet" you may be unable to hear it at all. Certainly you would never hear it near the horn of an ocean liner.

Sound Intensity is a measure of the acoustical power transmitted by the sound wave. Intensity is measured in terms of a certain section of the wave, specified as one square centimeter in scientific measurements. (There are 6.45 square centimeters in a square inch.)

Intensity is sound energy carried in one square centimeter of the wave

Any kind of power can be measured in watts. This is true of sound-waves. One-tenth of one quadrillionth of a watt (.000,000,000,000,0001 watt) of sound power passing through an area of one square centimeter is not quite audible, using a vibration frequency of 1000 cycles per second. One-quadrillionth of a watt (.000,000,000,000,001 watt), however, is easily audible. A sound that is loud enough to be almost painful represents an intensity of less than one-thousandth of a watt per square centimeter.

Scale of relative loudness

Every time that the intensity (or power) of a sound wave is multiplied by ten, it sounds louder by about the same amount. (It sounds as if a similar . "quantity" of sound has been added.) A change in intensity of ten times does not represent as great a change in loudness as one might expect. In fact, a change in intensity of 26% is just barely detectable. The range between the intensity at which a 1000-cycle sound is first heard (the threshold of hearing) and a point at which an increase in power ceases to give the impression of further increase in loudness is a trillion times. Thus each multiplication of ten in intensity is equivalent to about one-twelfth of the range from audibility to saturation.

When intensity is plotted on a log scale the left curve becomes a straight line (right)

Loudness increases by equal amounts not with equal additions of sound intensity, but rather with equal multiplications of intensity. In this respect, therefore, our response to a change in intensity is similar to our response to a change in frequency - it is logarithmic. (Note the similarity of the graph of intensity and loudness to the graph of frequency and pitch; both are plotted on a logarithmic scale.) The fact that this logarithmic relationship exists is generalized in a principle known as Fechner's Law, which states that "For a sensation to increase in arithmetic proportion, the stimulus must increase in geometric progression." Fechner's Law may be applied to the other senses as well as to hearing.

The basis of the loudness scale is a multiplication factor of 10. This unit (called a bel) is inconveniently large, since there are only 12 bels in the entire useful range of audibility at 1000 cycles. For this reason, a smaller unit, the decibel (one-tenth of a bel) is more commonly used. (Thus the range of useful audibility at 1000 cycles is 120 decibels.) The decibel (abbreviated db) is also a convenient unit because it represents the 26% intensity change that is the smallest possible change an average person can hear in the range of loudness at which the ear is most sensitive to change. Over most of the range a 2-db change is difficult to detect, and at higher levels an even greater change is necessary.

We respond to sound intensity logarithmically

Because our response to sound intensity is logarithmic, our impression of loudness can be quite deceiving. If, for example, we are listening to the radio at low volume, we may not realize just how low the volume is, until an airplane passes over. The radio seems to become even less loud as the sound of the airplane drowns it out and our ears become less sensitive to the quieter sound. (This effect, known as masking, will be discussed in greater detail later.) Our instinctive reaction when this occurs is to turn up the volume control.