Question
 A rifle shot is fired in a valley between two parallel walls. The echo from one wall is heard in 3 s and the echo from the other wall is heard 3 s later. If the velocity of sound at 00 c is $330 ms^{-1}$ and the temperature in the valley is 100 c , calculate the width of the valley. For every 10 c rise in temperature, the velocity of sound increase by $0.61 ms^{-1}$.

Answer

Give that, speed of sound at $0^{\circ}=330 \mathrm{~m} / \mathrm{s}$
For every $1^{\circ}$ rise in temperature, the velocity of sound increases by $0.61 \mathrm{~m} / \mathrm{s}$ $\therefore$ the velocity of sound at $10^{\circ}=330+(0.61 \times 10)=330+6.1=336.1 \mathrm{~m} / \mathrm{s}$
Let $A_1$ and $A_2$ be the distances of the two walls from the point of refile shots. Then
$ \begin{aligned} & 2 \times A_1=336.1 \times 3=1008.3 ...........(i) \\ & 2 \times A_2=336.1 \times 6=2016.6 ...........(ii) \end{aligned} $
Adding (i) and (ii) we get
$ 2\left(A_1+A_2\right)=3024.9 $
or, $\left(A_1+A_2\right)=1512.45 \mathrm{~m}$
Thus the width of the velley is $1512.45 \mathrm{~m}$

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