If you are new to the field of noise & vibration, the terms sound pressure, sound power, and sound intensity may be a bit confusing. This is understandable, as they are all commonly used, as well as interrelated… Not to mention they are all often expressed in decibels, which can be confusing in it’s own right. However, they each represent a different, important aspect of sound and how it is transmitted and experienced. In a three part series of posts, we will take a look at these three quantities of sound and see how they are all measured, calculated and used.
Sound pressure is the foundation of most acoustic work not only because it is a quantity analogous to our sense of hearing, but also because sound pressure measurements are one of the only measurements for sound one can actually make! As we’ll see, sound pressure measurements are the foundation of both sound power and sound intensity calculations.
When an object makes sound, it does so by vibrating back and forth. This causes the air molecules next to the object to vibrate as well. This vibrating chain reaction continues outward (at the speed of sound) away from the object in the form of waves. These waves are analogous to the waves formed in water when a pebble is dropped into a pond.
As the name suggests, we use the unit of pressure (Pascals, or Newton/meter^2) to quantify sound pressure. This value represents the summed amplitude of all the different sine waves that make up a sound (also called the “Overall Level”). It should be noted, however, that this pressure is really just the alternating portion of the pressure our ears (and microphones) are subject to. We also live under a huge amount of “static” pressure due to the earth’s gravitational pull on our atmosphere. This is commonly referred to as “atmospheric pressure.” Atmospheric pressure at sea level is about 101.3 kPa, or 194 dB!
However, because atmospheric pressure is constant for the most part, and since we are really only interested in the alternating portion of the pressure signal, we generally subtract atmospheric pressure and normalize sound pressure levels to be reported as the difference above/below zero. As we see in Figure 1 below, a normalized sound wave creates pressures that are both above and below zero, corresponding to the red and blue shaded regions respectively. Even though the normalized sound pressure is both positive and negative, we only report the amplitude of the pressure wave as being positive. This amplitude can be described using Peak, Peak-to-Peak, or RMS scaling. When we hear a sound, our brain acts as an integrator of these positive and negative oscillations, and we perceive a steady positive amplitude, we do not perceive the actual fluctuation of the individual sine waves.
Measuring Sound Pressure
A traditional engineering microphone detects sound waves in the air by measuring the displacement of a thin metallic membrane inside the microphone. This is very similar to how our ear works – our ears have a thin membrane called the ear drum that behaves the same way as a microphone membrane. The membrane begins to vibrate as the pressure waves reach the microphone - the larger the amplitude of the wave, the more displacement in the microphone membrane, the larger the signal sent from the microphone (Figure 2).
In Figure 2-A, we see small amplitude sound waves hitting the microphone, causing the microphone membrane to vibrate back and forth with a small amplitude. This relative motion between the membrane and an electrically charged disc called the “back plate” results in a capacitive difference. This difference generates a voltage output from the microphone that is proportional to the membrane displacement. In Figure 2-B, we see the same sound source outputting a higher amplitude sound wave, which causes the microphone membrane to vibrate with a higher amplitude, and thus output a larger voltage.
Just like the waves in the pond, the sound waves propagate away from the source in all directions. This causes the wave to spread out, and as a result the amplitude goes down as a function of distance. This is because we put a fixed amount of energy into the water with our pebble - for the amount of energy transferred to the water to remain constant, the amplitude of the wave must decrease as the wave front gets larger. This is also why things are louder up close: the amplitude of the sound waves is larger nearer to the source. As we move farther away, the same amount of energy is spread out over a larger area, so the amplitude gets smaller. In fact, when no reflections are present, the amplitude goes down by exactly half when we double our distance from the source. We are going to use this property of sound to our advantage for both sound power and sound intensity. Stay tuned for more!