Sound pressures are not atmospheric pressure, but small fluctuations above and below normal atmospheric pressure. This slide depicts a straight, horizontal line at the zero level, representing the atmospheric pressure as a reference. Around this line we see sound pressure fluctuations above and below the straight line. Note that the pressure fluctuations occur in symmetrical cycles. We have already seen that these cycles are related to a frequency, or pitch of the sound. Now we are interested in how far the fluctuations deviate from the reference line, because that determines how loud the sound is. There are several ways to describe these deviations. Two ways are shown here. We can simply measure the amplitudes of the peaks above or below the atmospheric pressure line. If they are symmetrical, as suggested by this slide, we can express a measure of loudness by this peak pressure value. This value is sometimes useful in determining potential for hearing damage, especially in short-duration sounds, such as a gunshot. The peak values occur rapidly and are short in duration, so that the human ear and brain do not have enough time to react to their harmful effects on the eardrum.
The peak value, however, is not a good measure of the perception of loudness. It reports the sound peak pressure but ignores the rest of the fluctuating pressures. One possible way to describe the entire sound signal would be to average the pressures. The problem with doing that is that the average of the sound pressures above and below the zero line will be zero. No matter how large the deviations may be, they will not be represented by the average value.
A more useful form of describing the sound signal is to use the root mean square value, depicted by the broken line paralleling the zero reference line. The calculation of the root mean square value takes all the positive and negative pressure in consideration and converts them to one positive value. With this calculation each value is first squared, making them all positive. Next the average, or mean, of the squared values is taken. Finally, the square root of the mean value is calculated. For a single frequency pressure waveform as shown in this illustration, the root mean square value is approximately 0.707 times the peak value. For a peak pressure of one million micro Pascal, the root mean square value would be approximately 707,000 micro Pascal.