Question

A steel tube of length 1.00 m is struck at one end. A person with his ear close to the other end hears the sound of the blow twice, one traveling 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

Hint: In the given we need to consider velocity of sound through air and velocity of sound through the body of the tube. We know that the velocity of sound through air is 330m/s and the velocity of sound through the tube is 5200 m/s.

Formula used:
$t=\dfrac{L}{v}$

Complete answer:
As we know,
Velocity of sound in air, ${{v}_{a}}=330m/s$
Velocity of sound through the body of the tube, ${{v}_{t}}=5200m/s$
Given, Length of the steel tube, $L=1m$

Let us assume, ${{t}_{1}}$and ${{t}_{2}}$ are the time taken by the sound to travel through air and sound travel through the steel tube respectively,
For the time taken by the sound to travel through air,
${{t}_{1}}=\dfrac{L}{{{v}_{a}}}$

For the time taken by the sound to travel through the steel pipe, ${{t}_{2}}=\dfrac{L}{{{v}_{t}}}$

Solving both the equation to get the value of \[{{t}_{1}}\]and ${{t}_{2}}$,
${{t}_{1}}=\dfrac{1}{330}$ and ${{t}_{2}}=\dfrac{1}{5200}$

Now, we have to find out the difference between \[{{t}_{1}}\]and ${{t}_{2}}$to get the final answer to the given question.
$T={{t}_{1}}-{{t}_{2}}$, Where $T$ is the value of difference between both the times taken through two different medium
$T=\dfrac{1}{330}-\dfrac{1}{5200}$$=2.75\times {{10}^{-3}}$$s$
$T=2.75ms$

Thus, the difference between the times taken by the sound to travel through two different mediums is 2.75ms.

Note: To tackle such a question we need to be well versed with speed of sound in air and several other mediums or else it will be provided with the question. Special care should be taken while putting values in such questions.