## Logarithmic Sound Levels Calculator

Sound Source | Typical dB Level |
---|---|

Threshold of hearing | 0 dB |

Whisper | 20 dB |

Normal conversation | 60 dB |

City traffic | 80 dB |

Rock concert | 110 dB |

Threshold of pain | 130 dB |

### Information:

Formula: Total dB = 10 * log10(Σ 10^(dB/10))

Adding two equal sound sources increases the level by 3 dB.

Every 10 dB increase represents a 10-fold increase in sound intensity.

Here's a comprehensive table with all the essential information about logarithmic sound levels:

Aspect | Information |
---|---|

Basic Formula | Total dB = 10 * log10(Σ 10^(dB/10)) |

Decibel (dB) | A logarithmic unit used to express the ratio of two values |

Reference Level | 0 dB = Threshold of human hearing (20 μPa in air) |

## Key Points:

- Every 3 dB increase doubles the sound intensity
- Every 10 dB increase is perceived as approximately twice as loud
- Adding two equal sound sources results in a 3 dB increase

## Logarithmic Addition Table:

Difference between two levels | Amount to add to the higher level |
---|---|

0 dB | 3.0 dB |

1 dB | 2.5 dB |

2 dB | 2.1 dB |

3 dB | 1.8 dB |

4 dB | 1.5 dB |

5 dB | 1.2 dB |

6 dB | 1.0 dB |

7 dB | 0.8 dB |

8 dB | 0.6 dB |

9 dB | 0.5 dB |

10 dB | 0.4 dB |

> 10 dB | 0 dB (negligible) |

## Common Sound Levels:

Sound Source | Typical dB Level |
---|---|

Threshold of hearing | 0 dB |

Rustling leaves | 20 dB |

Whisper | 30 dB |

Library | 40 dB |

Normal conversation | 60 dB |

Vacuum cleaner | 70 dB |

City traffic | 80 dB |

Lawn mower | 90 dB |

Rock concert | 110 dB |

Threshold of pain | 130 dB |

Jet engine at takeoff | 140 dB |

## Important Concepts:

- Sound Pressure Level (SPL): Measures the local pressure deviation from ambient atmospheric pressure
- Sound Power Level (SWL): Measures the total sound energy emitted by a source
- A-weighting (dBA): Adjusts sound measurements to correlate with human ear sensitivity

## Safety Guidelines:

Exposure Duration | Maximum Recommended Level |
---|---|

8 hours | 85 dB |

4 hours | 88 dB |

2 hours | 91 dB |

1 hour | 94 dB |

30 minutes | 97 dB |

15 minutes | 100 dB |

## Calculation Tips:

- To subtract decibels: 10 * log10(10^(dB1/10) - 10^(dB2/10))
- To average decibels: 10 * log10((Σ 10^(dB/10)) / n), where n is the number of measurements
- Sound level decreases by 6 dB each time the distance from the source doubles (inverse square law)

## Applications:

- Acoustics and noise control
- Audio engineering
- Environmental noise assessment
- Occupational health and safety
- Product design and testing

This table provides a comprehensive overview of logarithmic sound levels, including key concepts, common sound levels, safety guidelines, and practical calculation tips. This knowledge is crucial for acousticians, audio engineers, environmental scientists, and anyone working with sound measurements and noise control.