When determining the speed of sound in cast iron, a bell was struck at one end of a cast iron pipe

When determining the speed of sound in cast iron, a bell was struck at one end of a cast iron pipe, at the other end, the observer heard two sounds: first, one that came through the cast iron, and 2.5 s later, another that came through the air. The length of the pipe is 930 m. Determine the speed of sound in cast iron from this data. Take the speed of sound in air equal to 340 m / s.

Let us denote the length of the pipe through L, and the speed of sound in air and in cast iron through Vv and Vh.

Time of passage of sound to the observer through the air:
tв = L / Vв.

Time of passage of sound to the observer on cast iron:
tch = L / Vch.

Difference in travel time of sound through air and cast iron:
Δt = L / Vv – L / Vh;
L / Vv – Δt = L / Vh;
Vch = L / (L / Vv – Δt).

Substitute the values:
Vch = (930 m) / ((930 m) / (340 m / s) – 2.5 s) =
= (930 m) / (2.735 s – 2.5 s) =
= (930 m) / (0.235 s) =
= 3957.44 m / s.

Answer. The measured speed of sound in cast iron was 3957.44 m / s.