A physics Question on sound intensity

1. Learning Object 4
A family ice show is held in an enclosed arena. The skaters
perform to music with sound level 88.0 dB. This is too loud for
your baby, who consequently yells at a level of 83.0 dB.
1. What is the total sound intensity that you hear? (Answer in
W/m^2)
2. What is the combined sound level (Answer in dB)

2. Learning object 4 Solution:
The equation you will need is
1.
You can solve it by doing it in steps.
We can find the intensity of the music by
I_reference = 10^-12W/m^2
88dB= (10dB)log(I_music/I_reference)
Then isolating the log
88dB/10dB=log(I_music/I_reference)
The dB unit cancels And then taking the anti log
10^(88/10)= I_music/ 10^-12W/m^2
And then isolating I_music
by multiplying each side by the I_reference or 10^-12
(10^(88/10))*10^-12= I_music
which is equal to 6.3*10^-4 W/m^2
Now solving for the I_baby
You do the same process but with 83.0 dB instead of 88.0, so quickly :
(10^(83/10))*10^-12W/m^2= I_baby
which is equal to 2.0 *10^-4W/m^2
And then add them up to find the total intensity
2.0*10^-4 + 6.3*10^-4 = 8.3*10^-4 W/m^2
2.
Since you have the total intensity, you just plug it in back into the equation mentioned
above to find the total sound level:
And so,
SL= (10dB)log(8.3*10^-4/ 10^-12)
= 89.2 dB which is similar to being 10 metres away from a transport truck