Question

A steel tube of length $1m$ is struck at one end. A person with his ear close to the other end hears the sound of the blow twice, one travelling through the body of the tube and the other through the air in the tube. Find the time gap between the two hearings. Use the table in the text for speeds of sounds in various substances.

Answer 1

Step 1 Given data and assumptions.

Length of the steel tube $S=1m$

Time gap between the body of the tube$=t_1$

Time gap between the air in the tube$=t_2$

Step 2: Finding the time gap between the two hearings.

We know that,

Velocity of sound in air $v_{air}=330\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

Velocity of sound through the steel tube $v_s=5200\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

Now,

Required time gap,

$t=t_1-t_2$

$\Rightarrow$$t=\frac{S}{v_{air}}-\frac{S}{v_s}$ $\left[\because Time=\frac{Dis\tan ce}{Velocity}\right]$

$\Rightarrow$$t=\frac{1}{300}-\frac{1}{5200}$

$\Rightarrow$$t=2.75ms$

Hence, the time gap between the two hearings is $2.75ms$