Question

A hollow iron pipe is being hammered is heard at the other end at an interval of 0.5s, what is the length of iron pipe, if speed of sound in air is 320 m s${}^{-1}$ and that in iron is 4320 m s${}^{-1}$?

• A. 152.8 m
• B. 162.8 m
• C. 172.8 m
• D. 182.8 m

Answer 1

The correct option is C 172.8 m

Let $t_a$ be time taken in air and $t_1$ be the time taken in iron by the sound and $\Delta t=t_a-t_1=0.55$ velocity of sound in air $=320m{s}^{-1}$ velocity of sound in iron $4320m{s}^{-1}$.
If $\lambda$ is the length of iron pipe, then
$\Delta t=t_a-t_1=\frac{L}{V_s}-\frac{L}{V_i}$
$0.5=\frac{L}{320}-\frac{L}{4320}$
$\lambda =\frac{0.5\times 320\times 4320}{(4320-320)}$
$\lambda =172.8m$