How do decibels (dBs) work?

In How Environmental Noise is Measured we discussed how noise is largely characterised by measuring the Sound Pressure Level (SPL) and reporting this in decibels (dB).

Using decibels as our measurement unit means that we can measure sound on a logarithmic scale. To understand why a logarithmic scale is useful for measuring sound we first need to think about what ‘sound’ actually is.

What is sound?

Sound is a variation in pressure that is propagated as a wave through a medium. This can be any medium, but most of the time we think about sound as variations in air pressure, travelling through air.

Of course, sound can also travel through solids, such as wood and metal, or liquids. The properties of the medium affect the speed at which sound travels; that’s why everything sounds slightly odd underwater for example.

A chain of golf balls connected by strings

A nice way of trying to visualise a sound wave travelling through air is to imagine that the air particles are represented by a chain of golf balls connected together by springs.

If one of the golf balls is disturbed, this sets up a chain reaction – each ball, in turn, oscillates around its resting point (equilibrium position), and the disturbance is passed along the chain as a longitudinal wave.

It’s similar to the waves that sometimes happen in a crowd of people watching a sports event – a few people start the wave and it travels around the stadium, but the people themselves don’t move from their seating positions.

When the first air particle disturbed in the wave moves towards its nearest neighbour, the air pressure at that point increases – called compression.

As the air particle moves back again through its equilibrium position and to the other side, the air pressure between the two neighbouring particles decreases – this is rarefaction.

As the sound wave travels, regularly alternating areas of compression and rarefaction are set up.

This means that if we capture the sound wave at one stationary point (e.g. the point where you put your noise level meter) we can plot the air pressure variations against time, as illustrated in the picture above.

Image Credits: Many thanks to Dan Russell for making his fantastic acoustics animations freely available to the wider community. Dan works at Penn State University, USA, and has produced loads of really interesting animations about soundcheck them out.

How do we measure sound amplitude?

We discovered in the previous video that measuring environmental noise involves taking an average level at one location over a fixed period of time. We need to do this by calculating the average level of the sound wave in a particular way called the root mean square (RMS).

If we just took a simple mean average, by adding up all the pressure values over time and then dividing by the number of values we had, the positive values would in effect cancel out the negative values and leave us with an average of zero.

The root mean square (RMS)

But that doesn’t make much sense for us as we are trying to capture the effective amplitude of a wave. Taking the root mean square (RMS) value produces a better measure of the amount of pressure variation in the sound wave.

To do this we first square all the pressure values, which has the effect of making every value positive (so there are no longer any negatives cancelling out positives).

Then we take the average of the squares, and then take the square root of that average. This gives us an average value that much better represents the amplitude of the sound wave.

Calculating the RMS pressure amplitude of a sound wave is fairly simple, but it turns out that the range of pressure levels that we might want to measure in the world can vary over a huge range because the human ear is incredibly sensitive.

Calculating the RMS pressure

The human ear can detect sound pressure levels that range between:

• Just under 10 micro pascals (10 μPa or 10 × 10- 5 Pa): the threshold of human hearing
• Just over greater than 20 pascals (20 Pa): the threshold of pain
• That’s a range of over 2,000,000 (two million!) (note 1 Pascal is equal to a pressure of 1 newton per square metre (1 N m–2)) When we have a large range to measure it’s often much more efficient and clearer to use a logarithmic scale rather than a linear scale. On a linear scale the change between two values is based on the difference between them; for example, moving from 20 to 30 on a linear scale represents a difference of 10.

A logarithmic scale

On a logarithmic scale, however, the changes between two values are based on multiplication (or orders of magnitude). On our logarithmic Decibel scale, a sound measured at 30dB has 10 times greater acoustic pressure amplitude than a sound measured at 20dB.

There are lots of different things that engineers and scientists measure on a logarithmic scale because of the large range of values they need to capture, such as:

• The strength of earthquakes
• The intensity of light
• Sound pressure levels.

Here are some common examples of approximate sound pressure levels in decibels which should give you a good idea of how sensitive, and incredible, human hearing really is.

If you’d like to learn more about engineering the future, check out the full online course, from The University of York, below.