3

3. [Maximum mark: 6]

The loudness of a sound, $L$, measured in decibels, is related to its intensity, $I$ units, by $L = 10 \log_{10}(I \times 10^{12})$.

Consider two sounds, $S_1$ and $S_2$.
$S_1$ has an intensity of $10^{-6}$ units and a loudness of 60 decibels.
$S_2$ has an intensity that is twice that of $S_1$.

(a) State the intensity of $S_2$. [1]

(b) Determine the loudness of $S_2$. [2]

The maximum loudness of thunder in a thunderstorm was measured to be 115 decibels.

(c) Find the corresponding intensity, $I$, of the thunder. [3]