The case of pure tones and in-phase waves
When two sounds are added together, it’s not the decibels that are added directly, but the acoustic pressures. dBs are merely a mathematical translation of sound levels.
In the case of two pure, sinusoidal sounds of the same frequency and amplitude :
– If they are in phase, the amplitude doubles, resulting in a level of around 103 dB instead of 100 dB.
– If they are in phase opposition, the waves cancel each other out, which is equivalent to 0 dB.
– In the real world of manufacturing, situations fall somewhere between these two extremes.
Consistent sources and direct addition of pressures
When two sound sources are coherent, i.e. synchronized with a fixed phase and identical frequency, their acoustic pressures add directly to each other. This is the case, for example, with two loudspeakers fed by the same signal, or with an active noise reduction system. Under these conditions, the increase in noise level is significant and must be anticipated right from the design stage.
Inconsistent sources and logarithmic addition
In most industrial environments, sources are neither synchronized nor coherent. Their pressures vary independently, which means that sound intensities are added together, rather than instantaneous pressures.
The general formula for calculating the total level is :
Lp_total = 10 - log10 (10^(Lp1/10) + 10^(Lp2/10))
With:
– Lp = sound level in decibels
– I = sound intensity
– I0 = 10-¹² W/m², hearing threshold
This equation explains why two identical sources at 100 dB give approximately 103 dB, and not 200.
Addition of different sound levels
When two different levels are added together, the weaker source quickly becomes negligible. For example:
– 100 dB + 105 dB ≈ 106.2 dB
– 100 dB + 110 dB ≈ 110.4 dB
A difference of 10 dB means that the contribution of the weakest source is almost imperceptible in the total level. This phenomenon is a decisive factor in industrial acoustic studies and in the sizing of noise reduction equipment.
Acoustics at Groupe BOËT
Groupe Boët incorporates this acoustic complexity into every one of its solutions. Right from the diagnosis phase, our engineers take into account the logarithmic addition of sound levels to correctly size industrial silencers, Acoustic enclosures, absorbent panels or acoustic grilles. This rigor is backed up by a certified quality policy, with standards such as
Conclusion: transforming acoustic complexity into concrete solutions
The addition of sounds perfectly illustrates that industrial acoustics is based on non-intuitive physical principles. By understanding that decibels obey a logarithmic logic, it becomes possible to design truly effective acoustic protection systems. The Groupe BOËT supports manufacturers in this process, transforming mathematical complexity into tailor-made acoustic solutions.
👉 Would you like to find out more about our approaches or request an acoustic study tailored to your facilities? Contact Groupe BOËT today to benefit from our certified expertise.
