Find the decibel intensity level at a rock concert if the intensity was measured at 3.98x10^-3
To find the decibel intensity level at a rock concert, you need to use the logarithmic formula for sound intensity level:
I(dB) = 10 * log10(I/I0)
Where:
- I(dB) is the decibel intensity level
- I is the actual sound intensity
- I0 is the reference sound intensity, which is usually set as 1x10^-12 W/m^2
Given that the intensity (I) was measured at 3.98x10^-3 W/m^2, we can calculate the decibel intensity level as follows:
I(dB) = 10 * log10(3.98x10^-3 / 1x10^-12)
Using a calculator or a software program, calculate the logarithm of the ratio of the intensities:
I(dB) = 10 * log10(3.98x10^-3 / 1x10^-12) = 10 * log10(3.98x10^9) ≈ 89 dB
Therefore, the decibel intensity level at the rock concert is approximately 89 dB.
To find the decibel intensity level at a rock concert, you will need to use the formula:
I_dB = 10 * log10(I / I_0)
where:
I_dB is the decibel intensity level,
I is the measured intensity, and
I_0 is the reference intensity (threshold of hearing), which is generally 1x10^-12 W/m^2.
Given that the measured intensity is 3.98x10^-3, we can substitute these values into the formula:
I_dB = 10 * log10(3.98x10^-3 / 1x10^-12)
Calculating this expression:
I_dB ≈ 10 * log10(3.98x10^9) (using log10(a/b) = log10(a) - log10(b) )
I_dB ≈ 10 * (9.6) (taking the log10 of 3.98x10^9 is approximately 9.6)
I_dB ≈ 96 dB
Therefore, the decibel intensity level at the rock concert is approximately 96 dB.