91Ó°ÊÓ

Given data.

There is a gap of five seconds between the lightning flash and the following thunder that gives the distance to the flash in miles.

So, the sound is traveling one mile in 5 seconds.

You know that $\mathrm{Average}\mathrm{speed}=\frac{\mathrm{traveled}\mathrm{distance}}{\mathrm{time}}$.

Here, the distance traveled by the sound is 1 mile.

Now,

$\begin{array}{c}1\mathrm{mile}=1.6\mathrm{km}\\ =1.6\mathrm{km}×\frac{1000\mathrm{m}}{1\mathrm{km}}\\ =1600\mathrm{m}\end{array}$

(a) Then,

$\begin{array}{c}\mathrm{Average}\mathrm{speed}=\frac{1600\mathrm{m}}{5\mathrm{s}}\\ =320\frac{\mathrm{m}}{\mathrm{s}}\end{array}$

Therefore, the estimated speed of the sound is $320\frac{\mathrm{m}}{\mathrm{s}}$.

(b) Let the sound take $\mathrm{Δ}t$time to travel a distance of 1 km or 1000 m.

Then,

$\begin{array}{c}\mathrm{Δ}t = \frac{1 \mathrm{km}}{\mathrm{average}  \mathrm{speed}  \mathrm{of}  \mathrm{sound}}\\ =\frac{1000 \mathrm{m}}{320 \frac{\mathrm{m}}{\mathrm{s}}}\\ = 3.125 \mathrm{s}\\ ≈ 3 \mathrm{s}\end{array}$

Therefore, the rule is ‘every three seconds between a lightning flash and the following thunder gives the distance to the flash in kilometers.’