# Intensity of sound

1. May 23, 2010

### roam

1. The problem statement, all variables and given/known data

By what factor is the intensity of sound at a rock concert louder than that of a whisper when the two intensity levels are 120 dB and 20 dB respectively?

2. Relevant equations

The sound level of a sound wave in decibles is

$$\beta = 10 log (\frac{I}{I_0})$$

Also the ratio of intensities:

$$\beta_B - \beta_A = 10 log (\frac{I_B}{I_A})$$

3. The attempt at a solution

Using the latter equation:

$$100 = 10 log (\frac{I_B}{I_A})$$

Solving for the ratio I get 22026.4. Now how can I determine the factor one intensity is greater than the other? I'm not quite sure...

2. May 23, 2010

### rl.bhat

The equation should be

$$100 = 10log_{10}(\frac{I_A}{I_B})$$

Or $$10 = log_{10}(\frac{I_A}{I_B})$$

Now find the ratio of the intensities.

Last edited: May 23, 2010