A decibel meter reads 130 dB at a certain position from a jet plane when one engine is turned on.
a) What is the sound intensity at that position?
b) What would be the sound level at the same position if two engines are turned on each having the same intensity as the first?
Answer so far:
I = 10 lg(I/Io)
130 = 10 lg I - lg Io
130 = 10 (lg I - lg Io)
13 = lg I - lg Io
13 = lg I - lg (1*10^-12)
13 - 12 = lg I
1 = lg I
10^1 = I
10 W/m^2 = I
b) 2* 10 W/m^2 = 20 W/m^2
a. db = 10*Log(I/Io) = 130.
10*Log(I/10^-12) = 130.
Log(I/10^-12) = 13.
I/10^-12 = 10^13.
I = 10 W/m^2.
b. db = 10*Log(20/10^-12) = 133.
Doubling the sound intensity increases the sound level by only 3 db.
To answer question a), we need to determine the sound intensity at the given position. We can use the formula:
I = 10^(L/10)
where I is the sound intensity in watts per square meter (W/m^2) and L is the sound level in decibels (dB).
Given that the decibel meter reads 130 dB, we can substitute L = 130 into the formula:
I = 10^(130/10)
I = 10^13
I = 10,000,000,000,000 W/m^2
Therefore, the sound intensity at that position is 10,000,000,000,000 W/m^2.
Now, to answer question b), we are asked to calculate the sound level at the same position if two engines are turned on, each having the same intensity as the first engine.
Since the sound intensity of each engine is given as 10 W/m^2, the total sound intensity when both engines are turned on becomes:
I_total = 2 * 10 W/m^2
I_total = 20 W/m^2
To determine the sound level corresponding to the total sound intensity, we can rearrange the formula:
L = 10 * log10(I/Io)
where L is the sound level in decibels (dB), I is the sound intensity, and Io is the reference sound intensity, which is generally considered to be 10^-12 W/m^2.
Substituting I_total = 20 W/m^2 and Io = 10^-12 W/m^2 into the formula, we can solve for L:
L = 10 * log10(20/10^-12)
L = 10 * log10(2 * 10^13)
L = 10 * (log10(2) + log10(10^13))
L = 10 * (0.301 + 13)
L = 10 * 13.301
L = 133.01 dB
Therefore, the sound level at the same position when two engines with the same intensity as the first are turned on is 133.01 dB.