Calculating Total Sound Intensity and Combined Sound Level: Ice Show Example"

[RedPhoenix]

Homework Statement

A family ice show is held at an enclosed arena. The skaters perform to music with level 80.0 dB. This is too loud for your baby, who yells at 75.0 dB.

(a) What total sound intensity engulfs you?
(b) What is the combined sound level?

Homework Equations

dB = 10log(I/1E-12)

The Attempt at a Solution

I am trying to convert back, but I have never been great with logs, and I cannot figure out how to get I.

80=10log(I/1E-12)
75=10log(I/1E-12)

EDIT - it just clicked - anti-derivatives
A)
75db = 10^7.5/1E12 = I(b)
80db = 10^8/1E12 = I(m)
add them for total = 1.316E-4

B)
10log(1.316E-4/1E-12)
81.19dB

 

[Anden]

A hint: Use the fact that 10^log x = x

 

[nlightner]

To calculate the total sound intensity, we can use the equation dB = 10log(I/1E-12), where dB is the decibel level and I is the sound intensity in watts per square meter. By converting the decibel levels given in the problem to their corresponding sound intensities, we can add them together to find the total sound intensity. In this case, the sound intensity engulfing you would be 1.316E-4 W/m^2.

To calculate the combined sound level, we can use the same equation and convert the total sound intensity back to decibels. This can be done by taking the logarithm of the total sound intensity and multiplying it by 10. In this case, the combined sound level would be 81.19 dB. This indicates that the overall sound level is louder than either the music or the baby's yelling alone. It is important to consider the combined sound level in situations like this to ensure that the sound does not reach harmful levels.