Pressure Amplitude: Quantitative Measurement of Sound

As we will discuss in this section decibels are a means of creating a logarithmic scale relative to some reference. Decibel scales are by no means confined to acoustics, there are decibel scales defined for use in electronics and optics. Even in acoustics there are a variety of different definitions of the decibel scale depending upon the quantity being used as a reference. Thus, to begin our discussion I want to cover the question of what parameters are measured in determining sound levels.

The most physically understandable quantity used in determining the size of a sound signal is the Pressure Amplitude. Pressure amplitude is a measure of the size of the variation in air pressure caused by a sound wave. In pure silence there is a constant pressure--atmospheric pressure. Atmospheric pressure is measured in newtons/meter2 and is approximately 105 N/m2. The atmospheric pressure varies a small amount over the space of hours or days--this is what they mean by high and low pressure centers on the weather map--however, we can consider it to be essentially constant on the time scale of sound waves.

A sound wave creates a variation in the normally constant air pressure that oscillates above and below the normal atmospheric level of 105 N/m2. The average size of the pressure variation away from the constant background level is the Pressure Amplitude of the sound wave. I am hiding a bit of complication in the word average; the pressure goes above (positive) and below (negative) the constant atmospheric background so a straight average would tend to give zero. The real average is a root mean square average which you might be familiar with if you have done some electronics. For a pure tone--a pure sine wave--the averaging process leads to a pressure amplitude that is reduced from the maximum amplitude by a factor of 0.707 (equivalent to dividing by the square root of 2). The relation between amplitude of the sine wave (measured from the background level to one extreme) to the pressure amplitude (average pressure excursion from the background) is shown in the figure below.

It is fairly simple to understand how a calibrated measurement of the pressure amplitude can be made using a microphone to convert the pressure variations into an electrical signal. By applying known pressure variations to the microphone the electrical signal can be calibrated to directly measure the air pressure variations. With suitable processing this pressure variation can be converted into the pressure amplitude. This function is performed by Sound Pressure Level (SPL) meters.

Our next concern is to address the question: how large is the pressure amplitude for typical sounds? To answer we begin by considering the pressure amplitude for the weakest sound that is audible to the average person. This value is referred to as the threshold of hearing (for obvious reasons). The pressure amplitude for the threshold of hearing is 2 x 10^-5 N/m². This is a standard value defined for a pure sine wave at a frequency of 1000 Hz. As we will see later in this class, our ability to hear is a strong function of frequency so the value is quite different at other frequencies. Of course the ability to hear also varies from person to person so this is an average for the human population.

It is instructive to compare the threshold of hearing value to the background air pressure. Remember the pressure amplitude is the average size of the pressure variation on the constant atmospheric background. By taking the ratio of the threshold of hearing pressure amplitude to atmospheric pressure we see that the weakest audible sound waves only create a variation in the background pressure of 0.00000003%. Pretty small. Now how about very loud sounds. The threshold of pain corresponds roughly to a pressure amplitude of 30 N/m² (a million times larger than the threshold of hearing). This value translates to pressure variations of 0.03% about the atmospheric background value. Even loud sounds do not vary the background air pressure by even 1%!

Sound Pressure Level: A Decibel Scale defined in Terms of Pressure Amplitude

Now that we understand pressure amplitude as one measure of the size of a sound signal lets look at the decibel scale defined for this quantity. The decibel scale for pressure amplitude is called Sound Pressure Level, typically abbreviated SPL, and designated in our text and in this course by the symbol L_p