An equation for loudness L in decibels is given by L=10logR , where R is the relative intensity of the sound compared to the minimum threshold of human hearing. One city’s emergency weather siren is 138 decibels loud. How many times greater than the minimum threshold of hearing is the siren?
10 logR = 138
logR = 13.8
R = 10^13.8 ≈ 6.3 * 10^13
Well, if the equation for loudness is L=10logR, and the siren is 138 decibels loud, we can plug in the values and solve for R. Let's see:
138 = 10 * log(R)
Now, to isolate R, we'll divide both sides by 10 and then take the exponent of both sides:
log(R) = 138/10
log(R) = 13.8
Now, to get rid of the logarithm, we'll take both sides to the power of 10:
R = 10^13.8
After some calculation, we find that R is approximately equal to 6.31 x 10^13.
So, the siren is approximately 6.31 x 10^13 times greater than the minimum threshold of hearing. That's quite a blast!
To determine how many times greater than the minimum threshold of hearing the siren is, we need to find the relative intensity (R) for the given loudness of 138 decibels.
The equation for loudness (L) in decibels is given by L = 10 log R.
We can rearrange the equation to solve for R:
R = 10^(L/10)
Substituting the given loudness of the siren (L = 138 decibels) into the equation, we have:
R = 10^(138/10)
Calculating the value, we find:
R ≈ 3981071.705535
Thus, the relative intensity of the siren is approximately 3,981,071.705535 times greater than the minimum threshold of human hearing.
To determine how many times greater the siren is compared to the minimum threshold of hearing, we need to use the equation:
L = 10 log R
Given that the loudness of the siren (L) is 138 decibels, we can substitute this value and solve for R:
138 = 10 log R
To isolate R, we divide both sides of the equation by 10:
13.8 = log R
Now, we need to convert the logarithmic equation into an exponential equation. We raise both sides of the equation to the power of 10:
10^13.8 = R
Using a calculator, we find that 10^13.8 is approximately 398107170.55.
Therefore, the relative intensity of the siren (R) is approximately 398107170.55 times greater than the minimum threshold of hearing.