When two sound sources play simultaneously, the total sound level, or the total number of decibels (dB), is not simply the sum of the individual decibel levels. Instead, it follows a logarithmic scale called the "decibel addition rule" or "logarithmic addition."
The decibel scale is logarithmic because our perception of sound intensity follows a logarithmic relationship with the actual physical intensity. The formula to calculate the total decibel level when two sound sources are combined is:
L_total = 10 * log10(10^(L1/10) + 10^(L2/10))
where L_total is the total sound level in decibels, L1 is the decibel level of the first sound source, and L2 is the decibel level of the second sound source.
Using this formula, let's calculate the total number of decibels when two 40 decibel speakers are playing simultaneously:
L_total = 10 * log10(10^(40/10) + 10^(40/10)) = 10 * log10(10^4 + 10^4) = 10 * log10(10000 + 10000) = 10 * log10(20000) ≈ 10 * 4.301 ≈ 43.01 dB
Therefore, when two 40 decibel speakers are playing at the same time, the total sound level would be approximately 43.01 decibels.