# Adding Decibels

## The logarithmic decibel scale is convenient calculating sound power levels and sound pressure levels for two or more sound sources

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### Adding Equal Sound or Noise Power Sources

The resulting sound power when adding equal sound power sources can be expressed as:

L_{wt}= 10 log(n N / N_{0})

= 10 log(N / N_{0}) + 10 log(n)

= L_{ws}+ 10 log(n)(1)

where

L_{wt}= the total sound power level (dB)

L_{ws}= sound power level from each single source (dB)

N= sound power (W)

N_{0}= 10^{-12}- reference sound power (W)

n = number of sources

#### Adding Equal Sound Power Calculator

Adding of equal sound power sources can be expressed graphically

**Note!** Adding of two identical sources will increase the total sound power level with 3 dB (10 log(2)).

Sound power and sound power level are often used to specify the noise or sound emitted from technical equipment like fans, pumps or other machines.

Sound measured with microphones or sensors are sound pressure.

### Adding Equal Sound Pressure Levels

The resulting sound pressure level when adding equal sound pressure can be expressed as:

L_{pt}= L_{ps}+ 20 log(n)(2)

where

L_{pt}= total sound pressure level (dB)

L_{ps}= sound pressure level from each single source (dB)

n= number of sources

#### Adding Equal Sound Pressure Levels Calculator

Number of Sources | Increase in Sound Power Level (dB) | Increase in Sound Pressure Level (dB) |
---|---|---|

2 | 3 | 6 |

3 | 4.8 | 9.6 |

4 | 6 | 12 |

5 | 7 | 14 |

10 | 10 | 20 |

15 | 11.8 | 23.6 |

20 | 13 | 26 |

### Adding Sound Power from Sources with different Sound Powers

The sound power level from more than one source can be calculated as

L_{wt}= 10 log( (N_{1}+ N_{2}... + N_{n}) / N_{o})(3)

Adding two sources at different levels can be expressed graphically as

Sound Power Level Difference between two Sound Sources (dB) | Added Decibel to the Highest Sound Power Level (dB) |
---|---|

0 | 3 |

1 | 2.5 |

2 | 2 |

3 | 2 |

4 | 1.5 |

5 | 1 |

6 | 1 |

7 | 1 |

8 | 0.5 |

9 | 0.5 |

10 | 0.5 |

> 10 | 0 |

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