Two noises produce sound levels of 70 and 80 dB when acting separately. Find the sound level in dB when the sources act together.
To find the sound level when the sources act together, we need to understand the concept of sound levels and how they combine.
Sound level, measured in decibels (dB), is a logarithmic scale that represents the intensity of sound. When two sound sources act together, their sound levels add up. This phenomenon is known as the logarithmic addition of sound levels.
To calculate the combined sound level, we can use the formula:
L_total = 10 * log10(10^(L1/10) + 10^(L2/10))
Where L_total is the total sound level when the sources act together, L1 and L2 are the individual sound levels of the two sources.
In this case, the two sound levels are 70 dB and 80 dB when acting separately.
L1 = 70 dB
L2 = 80 dB
Plugging these values into the formula, we get:
L_total = 10 * log10(10^(70/10) + 10^(80/10))
Simplifying the equation:
L_total = 10 * log10(10^7 + 10^8)
Now, we can calculate the values inside the logarithm:
L_total = 10 * log10(10,000,000 + 100,000,000)
Adding the numbers inside the parentheses:
L_total = 10 * log10(110,000,000)
Calculating the logarithm:
L_total = 10 * 8.04139
Multiplying:
L_total ≈ 80.414 dB
So, when the two noises act together, the sound level is approximately 80.414 dB.