# Fundamentals of Acoustics: Sound Pressure, Sound Power and Sound Intensity

By Marshall Williams 26 January 2021

There are lots of ways to quantify sound. Three of the main terms used are sound pressure, sound power and sound intensity. This blog aims to explain the difference between these terms and how they all relate to one another.

## Sound Pressure

Sound pressure or acoustic pressure is a scalar quantity used to indicate the amplitude level of  sound at a specific location in space. It is the deviation from the ambient atmospheric pressure and is caused by a sound wave. Sound pressure depends on the distance the measurement is taken from and in what atmospheric environment it is taken in. The SI units for sound pressure is the Pascal (Pa). In air, sound pressure can be measured using a microphone and in water with a hydrophone. The human ear can tolerate a very large range of sound pressures, however, the minimum sound pressure possible for a human to hear is ~20 µPa. Although, damage to the ear through disease or loud music can affect the sensitivity. Typically, ear discomfort is experienced at ~20 Pa and ear pain is experienced at a sound pressure of ~60 Pa. To put this into perspective, 20 Pa is the typically the sound pressure at a rock concert and 60 Pa is the equivalent of someone blowing a trumpet into your ear from 0.5 m away.

Sound pressure is also commonly given in decibels (dBs) for a couple of reasons; a lot of common day-to-day sounds have very small sound pressure values, such as a normal conversion at 0.01 Pa; and the range typically runs from µPa to kPa which is a large range. When expressed using decibels it is referred to as sound pressure level. Decibels are not a unit of measure but a logarithmic function which indicates the ratio between two values. When measuring sound pressure level, we use the equation:

Sound Pressure Level=20log10(p⁄pref ) dB

Where p is sound pressure measured and pref is the universally agreed upon reference sound pressure, 20 µPa (remember, this is the smallest sound we can hear). So, for a normal conversation the sound pressure is 0.01 Pa, and the sound pressure level is 54 dB. Another benefit of using decibels to express sound pressure is that the logarithmic scale means the numerical range of the sound pressure is smaller and more manageable.

## Sound Power

Sound power is the rate at which sound energy is emitted from a source per unit time. This produces sound pressure at some distance from the source. Sound power has SI units watts (W). This measurement is often used in the noise regulations for construction equipment so that employers can ensure that their employees are well equipped and safe to work in the environment. Sound power is a useful measurement as it is independent of distance from source and location of microphone. Quantifying sound power is therefore a more complex task but is commonly done using multiple microphones placed around the object in a semi hemisphere set up to capture the sound emitted from all around the object in all directions. As with sound pressure, sound power level is often quantified in decibels and is given by the equation:

Sound Power Level=10log10(p⁄pref ) dB

Where P is the sound power and Pref is the universally agreed upon reference sound power, 1 pW. However, often nowadays sound power level is given in bels (1 bel = 10 decibels) so as not to confuse with sound pressure level.

## Sound Intensity

Sound intensity is the sound power per unit area and indicates the flow of sound through a specific area in a direction. The SI Unit is W/m2. Sound intensity is directly related to sound pressure:

Sound Intensity=Sound Pressure x Particle Velocity

Where particle velocity is the speed and direction in which the particles in the medium vibrate back and forth when transmitting sound. Sound intensity is often used as a measurement in audio electronics as not only does the “loudness” (i.e. the pressure level) matter, but also the direction in which that “loudness” propagates. Measuring sound intensity is similar to sound power as it requires two or more microphones in an arrangement to capture the amplitude and direction.

Sound intensity level is also commonly quantified in decibels and is given by the equation:

Sound Intensity Level=10log10(I⁄Iref )  dB

Where I is the sound intensity and Iref is the universally agreed upon reference sound power, 1 pW/m2. Sound Intensity and sound power are related by the following equation:

Sound Intensity Level=Sound Power Level / Area

To conclude, sound pressure, sound power and sound intensity are fundamental terms used to quantity acoustics and are often given in decibels. They all describe different aspects of sound. The next step in our fundamentals of acoustics blog series is sound fields!