Question

I’ve been working on these similar questions but coming to this question. I found myself being stuck.

Answer 1

If the variation in pressure is P pounds per square inch, then the Loudness L in decibels is;

`L=20\log _(10)(121.3P)`

When L=115 decibels;

`\begin{gathered} 115=20\log _(10)(121.3P) \\ \text{Divide both sides by 20;} \\ (115)/(20)=(20\log_(10)(121.3P))/(20) \\ \log _(10)(121.3P)=5.75 \end{gathered}`

But from the logarithmic law, we have;

`\log _ba=c\leftrightarrow a=b^c`

Thus,

`\begin{gathered} \log _(10)(121.3P)=5.75 \\ 121.3P=10^(5.75) \\ 121.3P=562341.33 \end{gathered}`
`\begin{gathered} \text{Divide both sides by 121.3;} \\ (121.3P)/(121.3)=(562341.33)/(121.3) \\ P\cong4635.95 \end{gathered}`

FINAL ANSWER:

`4636.0\text{ pounds per square inch.}`