Question 697098
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*log((I/I[o]))}}} in general, measured by comparison to a reference level of {{{I[o]}}}.
On the highway, we have {{{beta(h)=10*log((I[h]/I[o]))}}}
On the runway, we have {{{beta(r)=10*log((I[r]/I[o]))=91}}}db
If {{{I[r]/I[h]=6420/4}}} <--> {{{I[h]/I[r]=4/6420)}}}
{{{beta(h)=10*log((I[h]/I[o]))=10*log(((I[r]/I[o])(I[h]/I[r])))=10*(log((I[r]/I[o]))+log((I[h]/I[r])))=10*log((I[r]/I[o]))+10*log((I[h]/I[r]))=91+10log(4/6420)=91+10*(-3.2)=91-32=59}}}dB
If {{{I[r]/I[h]=6420.4}}} <--> {{{I[h]/I[r]=1/6420.4)}}}, then
{{{beta(h)=91+10log(1/6420.4)=91+10*(-log(6420.4))=91-10*3.8=91-38=53}}}dB
 
{{{H}}} = hydronium ion concentration in mol/L
{{{pH=-log(H)}}}
{{{pH[1]=-log(4.4*10^(-8))=7.36}}} if we round to two decimal places.
Otherwise {{{pH[1]=7.3565
{{{pH[2]=-log(5.7*10^(-8))=7.24}}} if we round to two decimal places.
Otherwise {{{pH[1]=7.2441
Rounding intermediate calculations to the same number of decimal places would lead to rounding errors.
{{{pH[1]-pH[2]=7.3565-7.2441=0.1124=highlight(0.11)}}} (rounded)
 
It could be calculated all at once, without intermediate calculations:
{{{pH[1]-pH[2]=-log(4.4*10^(-8))-(-log(5.7*10^(-8)))=log(5.7*10^(-8))-log(4.4*10^(-8))=log(5.7*10^(-8)/(4.4*10^(-8)))=log(5.7/4.4)=log(1.295)=highlight(0.11)}}} (rounded)