The sound level when one child is talking in a room is 60.0 dB. What would be the sound level if all 20 children talk at the same time in the same room? Assume each child talks equally loudly.
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To find the sound level when all 20 children talk at the same time in the same room, we need to understand how sound levels combine.
Sound levels are measured in decibels (dB), and they follow a logarithmic scale. The formula to calculate the combined sound level of multiple sound sources is:
L₁ = 10 * log₁₀(N₁)
Where L₁ is the resulting sound level when N₁ sound sources are combined.
In this case, we have 20 children talking with the same sound level of 60.0 dB. Since each child talks equally loudly, we can assume their sound levels are the same.
Plugging in the values into the formula, we get:
L₁ = 10 * log₁₀(20)
Now let's calculate it step by step:
Step 1: Calculate log₁₀(20)
This step involves finding the logarithm of 20 to the base 10. The logarithm of a number is the exponent to which the base must be raised to yield that number. In this case, we want to find the exponent to which 10 must be raised to get 20.
log₁₀(20) ≈ 1.301
Step 2: Multiply the result by 10
L₁ = 10 * 1.301
L₁ ≈ 13.01
Therefore, the resulting sound level when all 20 children talk at the same time in the same room would be approximately 13.01 dB.