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 00c is 330 ms^-1 and the temperature in the valley is 100c, calculate the width of the valley. For every 10c rise in temperature, the velocity of sound increase by 0.61 ms^-1.

Answer 1

Give that, speed of sound at 0° = 330 m/s

For every 1° rise in temperature, the velocity of sound increases by 0.61 m/s

`therefore` the velocity of sound at 10° = 330 + (0.61 x 10) = 330 + 6.1 = 336.1 m/s

Let A₁ and A₂ be the distances of the two walls from the point of refile shots. Thhen 

2 x A₁ = 336.1 x 3 = 1008.3 ...................(i)

2 x A₂ = 336.1 x 6 = 2016.6 ...................(ii)

Adding (i) and (ii) we get

2 (A₁ + A_{2) =} 3024.9

or, (A₁ + A₂) = 1512.45 m

Thus the width of the velley is 1512.45 m