decibel question

Question

 

 

if a speaker is playing music at 45 decibels, what is the decibel reading of 6 identical speakers?

Answer 1

1. I(dB) = 10log₁₀ (I/I₀)   {For one speaker}
2. I_Total = 6I    {Total sound Intensity is equal to 6 times the intensity of one speaker}
3. I(dB) = 10log₁₀ (I_Total / I₀) =  10log₁₀ (6I / I₀)    {Eqn 1}
4. Use the Logarithm of a Product Property to rewrite Eqn 1:  I(dB) = 10 log₁₀ (6) + 10log₁₀ (I/I₀)
5. I(dB) = 7.8 + 45 = 52.8 dB