[Acoustics] Decibel Scale

2021-10-30 19:43 作者:AoiSTZ23 0人读过 | 我要投稿

By: Tao Steven Zheng (郑涛)

The decibel (dB) is a measure of the ratio between two quantities, and is used in a wide variety of measurements in acoustics. The decibel is used for measuring of the loudness of sound.

【Problem】

A police car siren measures 70 dB to someone 44 meters away. What is the sound level of the police car if the police car is 1 meter away from the person? Round to the nearest decibel.

【Solution】

There are two formulas that are useful for this problem：

1) $%5Cbeta%20%3D%2010%20%5Clog%20%5Cleft(%5Cfrac%7BI%7D%7BI_0%7D%5Cright)$ where $%20I_0%20%3D%20%7B10%7D%5E%7B-12%7D%20%5C%2C%20%5Cfrac%7BW%7D%7Bm%5E2%7D$

2) $P%20%3D%204%5Cpi%20r%5E2%20I%20$

First, solve for the intensity at 44 meters.

$70%20%3D%2010%20%5Clog%20%5Cleft(%5Cfrac%7BI%7D%7B%7B10%7D%5E%7B-12%7D%7D%5Cright)$

$I%20%3D%20(10%5E7)(%7B10%7D%5E%7B-12%7D)%20%3D%20%7B10%7D%5E%7B-5%7D%20%5C%2C%20%5Cfrac%7BW%7D%7Bm%5E2%7D%20$

Second, solve for the power, which is the same at any distance away from the sound source.

$P%20%3D%204%5Cpi%20(%7B10%7D%5E%7B-5%7D)%20%7B(44)%7D%5E%7B2%7D$