SOLUTION: The intensity level, β, in decibels, of sound is defined as β=10log(I/Io), where I is the instensityof the sound in watts per square metre. The ratioof the intensity of s

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: The intensity level, β, in decibels, of sound is defined as β=10log(I/Io), where I is the instensityof the sound in watts per square metre. The ratioof the intensity of s      Log On


   

Question 697098: The intensity level, β, in decibels, of sound is defined as β=10log(I/Io), where I is the instensityof the sound in watts per square metre. The ratioof the intensity of sound pollution measured at a small airport runway versus that of the local highway is 6420,4. If the sound level on the local highway is 91 dB, determine the sound level on the runway. to the nearest decibel.
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Find the difference in pH levels of a swimming pool with a hydronium ion concentration of 4.4 x 10^(-8) mol/L and a swimming pool with a hydronium ion concentration of 5.7 x 10^(-8) mol/L, to the nearest hundredth.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I do not understand what was meant by "the ratio of the intensity of sound pollution measured at a small airport runway versus that of the local highway is 6420,4," but I will use my two best guesses.

beta=10%2Alog%28%28I%2FI%5Bo%5D%29%29 in general, measured by comparison to a reference level of I%5Bo%5D.
On the highway, we have beta%28h%29=10%2Alog%28%28I%5Bh%5D%2FI%5Bo%5D%29%29
On the runway, we have beta%28r%29=10%2Alog%28%28I%5Br%5D%2FI%5Bo%5D%29%29=91db
If I%5Br%5D%2FI%5Bh%5D=6420%2F4 <--> I%5Bh%5D%2FI%5Br%5D=4%2F6420%29
dB
If I%5Br%5D%2FI%5Bh%5D=6420.4 <--> I%5Bh%5D%2FI%5Br%5D=1%2F6420.4%29, then
beta%28h%29=91%2B10log%281%2F6420.4%29=91%2B10%2A%28-log%286420.4%29%29=91-10%2A3.8=91-38=53dB

H = hydronium ion concentration in mol/L
pH=-log%28H%29
pH%5B1%5D=-log%284.4%2A10%5E%28-8%29%29=7.36 if we round to two decimal places.
Otherwise pH%5B1%5D=7.3565%0D%0A%7B%7B%7BpH%5B2%5D=-log%285.7%2A10%5E%28-8%29%29=7.24 if we round to two decimal places.
Otherwise (rounded)

It could be calculated all at once, without intermediate calculations:
(rounded)