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 0°C is 330 ms⁻¹ and the temperature in the valley is 10°C, calculate the width of the valley. For every 1°C rise in temperature, the velocity of sound increase by 0.61 ms⁻¹.

Answer 1

Given: \[ v_{0^\circ C}=330\ \text{m s}^{-1} \]

Temperature \(=10^\circ C\)

Increase in speed = \[ 0.61\times10=6.1\ \text{m s}^{-1} \]

So,

v = 330 + 6.1

= 336.1 ms⁻¹

For the first wall:

\[ d_1=\frac{vt_1}{2}\]

\[= \frac{336.1\times3}{2}\]

\[= 504.15\ \text{m}\]

The second echo is heard 3 s later, so its total time is:

t₂ = 3 + 3

= 6 s

\[ d_2=\frac{336.1\times6}{2} \]

= 1008.3 m

Therefore, width of the valley (W):

W = d₁ + d₂ 

= 504.15 + 1008.3

= 1512.45 m