A whisper in a Quiet library is about 30 decibels. What decibel level would be recorded by a table of 10 library patron each whispering at 30 decibels?
Would the answer be 40?
add 10 log power ratio
10 log 10 = 10
so yes 40
No, the answer wouldn't be 40 decibels. When multiple sound sources of the same volume are present, you cannot simply add their decibel levels together. The decibel scale is logarithmic, not linear.
In this case, if each library patron is whispering at 30 decibels, the combined sound level would only increase by about 3 decibels, resulting in approximately 33 decibels. So, the recorded decibel level would be around 33, not 40. Keep those whispers hushed!
No, the decibel level would not be 40. When multiple sound sources are present, their decibel levels do not simply add up. Instead, you need to use a logarithmic formula called the "logarithmic sum" to calculate the total decibel level. The formula is as follows:
L_total = 10 * log10(10 ^ (L1/10) + 10 ^ (L2/10) + ... + 10 ^ (Ln/10))
In this case, L1 represents the decibel level of the first person whispering (30 decibels), L2 represents the decibel level of the second person, and so on, up to Ln, which represents the decibel level of the last person.
Assuming all 10 patrons are whispering at 30 decibels each, the calculation would be:
L_total = 10 * log10(10 ^ (30/10) + 10 ^ (30/10) + ... + 10 ^ (30/10))
When you solve this equation, you will find that the total decibel level is approximately 34 decibels. Therefore, the answer is 34, not 40.
To determine the decibel level recorded by a table of 10 library patrons, each whispering at 30 decibels, you cannot simply add the decibel levels together. Decibels are measured on a logarithmic scale, not a linear scale.
To calculate the total decibel level, you need to use the formula for combining decibel levels in this scenario, which is:
L_total = 10 * log10(N * 10^(L1/10))
Where:
L_total is the total decibel level
N is the number of sound sources (in this case, 10 patrons)
L1 is the decibel level of each sound source (in this case, 30 decibels)
Using this formula, let's calculate the total decibel level:
L_total = 10 * log10(10 * 10^(30/10))
= 10 * log10(10 * 10^3)
= 10 * log10(10 * 1000)
= 10 * log10(10000)
= 10 * 4
= 40 decibels
So in this case, the total decibel level recorded by a table of 10 library patrons each whispering at 30 decibels would indeed be 40 decibels.