No, the result would not be 400 dB of sound.
The decibel (dB) scale is logarithmic, which means it is based on powers of 10. When combining sound sources, the decibel scale does not add up in a simple arithmetic manner.
For identical sound sources that are perfectly in phase, the resulting sound pressure level (SPL) will increase by about 6 dB for each doubling of the number of sources. This is known as a 6 dB increase per doubling of sources.
In your example, since you have four speakers, each emitting 100 dB of sound, the addition of the four speakers would result in an increase of approximately 6 dB, not 400 dB. Therefore, the resulting sound level would be around 106 dB.
The calculation would be as follows:
- For a single speaker emitting 100 dB, the SPL is 100 dB.
- When you add a second speaker (identical and perfectly in phase), you gain 6 dB, resulting in a total SPL of 106 dB.
- Adding a third speaker would again increase the SPL by 6 dB, resulting in a total SPL of 112 dB.
- Finally, adding a fourth speaker would increase the SPL by another 6 dB, giving a total SPL of around 118 dB.
So, in this scenario, the total sound level would be approximately 118 dB, not 400 dB.