## How to Calculate The Standing Waves

As we’ve discussed, whenever audio mastering (or carrying out other forms of music production) we’re at the whim of the acoustical effects of the walls, floor and ceiling. Left unchecked, these surfaces reflect sounds back into the room and towards our ears. These reflections cause us to hear additional information that may lead to a misinterpretation of the direct speaker sound because of their interaction with each other and the dimensions of the studio.

To calculate standing waves in a studio, first imagine how the standing waves behave: Sound waves travel through the air in alternating stages of high pressure and low pressure. Once a sound wave has begun travelling through the air (and let’s imagine a simple sine wave for this), it reaches its peak power of high pressure, dips to a pressure of zero then begins a period of low pressure, which again returns to zero (back to the starting point). The distance across the air from the sound source that it takes the wave to complete this full cycle is known as the wavelength. Low frequencies have a longer wavelength than high frequencies.

It’s known that the speed of sound through air at room temperature is** 344 metres per second**. The number of full wavelength cycles that can happen per second at a given frequency (or put another way, how frequently the full wave occurs per second) is measured in **Hertz (Hz)**. We’re able to measure the dimensions of a room in metres, and then calculate the frequencies that may be resonant, causing them to sound louder than they should.

A resonant frequency – in terms of this guide – is a frequency that is amplified by the dimensions of a room. Let’s imagine we have two flat parallel walls that are 4 metres apart. Any distance, including 4 metres, must be able to perfectly contain a sound wave frequency. This is the formula to discover which particular frequency it is:

Speed of sound (in metres per second) / distance between walls (in metres) = frequency (in Hertz)

So for the above scenario: 344m/s ÷ 4m = 86 Hz

This tells us that one full wavelength at 86 Hz exists between our two walls, bouncing back and forth and reinforcing the energy from the speakers more so than other frequencies and making it around 3dB louder than it should ideally sound. However, this isn’t the full story. As well as 86 Hz, half of this measured frequency is also able to reinforce, as will doubling 86 Hz, quadrupling, and so on. This means that as well as 86 Hz, we will be incorrectly hearing 43 Hz (half the frequency, twice the wavelength), 172 Hz (twice the frequency, half the wavelength), 344 Hz (four times the initial frequency, quarter the wavelength), and upwards within our studio, These waves at these frequencies will become standing waves in our studio.

Next chapter… **Tonal/Spectral Processing**