In speaking of sound perception, it’s important to distinguish between words which describe objective measurements and those that describe subjective experience.
The terms intensity and pressure denote objective measurements that relate to our subjective experience of the loudness of sound. Intensity, as it relates to sound, is defined as the power carried by a sound wave per unit of area, expressed in watts per square meter (W/m2). Power is defined as energy per unit time, measured in watts (W). Power can also be defined as the rate at which work is performed or energy converted. Watts are used to measure the output of power amplifiers and the power handling levels of loudspeakers. Pressure is defined as force divided by the area over which it is distributed, measured in newtons per square meter (N/m2)or more simply, pascals (Pa). In relation to sound, we speak specifically of air pressure amplitude and measure it in pascals. Air pressure amplitude caused by sound waves is measured as a displacement above or below equilibrium atmospheric pressure. During audio recording, a microphone measures this constantly changing air pressure amplitude and converts it to electrical units of volts (V), sending the voltages to the sound card for analog-to-digital conversion. We’ll see below how and why all these units are converted to decibels.
The objective measures of intensity and air pressure amplitude relate to our subjective experience of the loudness of sound. Generally, the greater the intensity or pressure created by the sound waves, the louder this sounds to us. However, loudness can be measured only by subjective experience – that is, by an individual saying how loud the sound seems to him or her. The relationship between air pressure amplitude and loudness is not linear. That is, you can’t assume that if the pressure is doubled, the sound seems twice as loud. In fact, it takes about ten times the pressure for a sound to seem twice as loud. Further, our sensitivity to amplitude differences varies with frequencies, as we’ll discuss in more detail in Section 4.1.6.3.
When we speak of the amplitude of a sound, we’re speaking of the sound pressure displacement as compared to equilibrium atmospheric pressure. The range of the quietest to the loudest sounds in our comfortable hearing range is actually quite large. The loudest sounds are on the order of 20 Pa. The quietest are on the order of 20 μPa, which is 20 x 10-6 Pa. (These values vary by the frequencies that are heard.) Thus, the loudest has about 1,000,000 times more air pressure amplitude than the quietest. Since intensity is proportional to the square of pressure, the loudest sound we listen to (at the verge of hearing damage) is $$10^{6^{2}}=10^{12} =$$ 1,000,000,000,000 times more intense than the quietest. (Some sources even claim a factor of 10,000,000,000,000 between loudest and quietest intensities. It depends on what you consider the threshold of pain and hearing damage.) This is a wide dynamic range for human hearing.
Another subjective perception of sound is pitch. As you learned in Chapter 3, the pitch of a note is how “high” or “low” the note seems to you. The related objective measure is frequency. In general, the higher the frequency, the higher is the perceived pitch. But once again, the relationship between pitch and frequency is not linear, as you’ll see below. Also, our sensitivity to frequency-differences varies across the spectrum, and our perception of the pitch depends partly on how loud the sound is. A high pitch can seem to get higher when its loudness is increased, whereas a low pitch can seem to get lower. Context matters as well in that the pitch of a frequency may seem to shift when it is combined with other frequencies in a complex tone.
Let’s look at these elements of sound perception more closely.