Question

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

Answer 1

We need to use our knowledge on the travelling techniques and speeds in different media of the sound waves to solve this problem. We can easily find the time gap between the delay of sound in reaching through one medium with respect to the other.

Complete answer:
We know that sound waves are longitudinal waves which propagate through a medium by the parallel movement of particles in the medium. As the propagation is dependent on the particles in the medium, the sound propagation is also medium dependent. It’s physical properties such as speed of wave propagation is highly dependent on the medium in which it travels.
The sound waves travel faster through solid and liquids than through the air. The particle nature of the solids is the best medium for sound propagation. The speed of sound through different metals also differs.
Here, we are given a steel tube and the air as the two media through which the sound travels. The sound travels the same distance of 1m but has a delay when moving through the air as we have explained earlier.
Now, we can find the time gap by using the speed of sound in steel and air.
The speed of sound in steel,
${{v}_{steel}}=5941m{{s}^{-1}}$
The speed of sound in air at room temperature,
${{v}_{air}}=343m{{s}^{-1}}$
The time taken by sound in steel tube is –

& {{t}_{steel}}=\dfrac{Length}{{{v}_{steel}}} \\\ & \Rightarrow {{t}_{steel}}=\dfrac{1}{5941} \\\ & \Rightarrow {{t}_{steel}}=168\mu s \\\ \end{aligned}$$ The time taken by sound in air is – $$\begin{aligned} & {{t}_{air}}=\dfrac{Length}{{{v}_{air}}} \\\ & \Rightarrow {{t}_{air}}=\dfrac{1}{343} \\\ & \Rightarrow {{t}_{air}}=2915\mu s \\\ \end{aligned}$$ Now, the time gap is given as – $$\begin{aligned} & {{t}_{gap}}={{t}_{air}}-{{t}_{steel}} \\\ & \Rightarrow {{t}_{gap}}=2915-168 \\\ & \therefore {{t}_{gap}}=2.747ms \\\ \end{aligned}$$ The air takes an additional 2.747ms to reach the listener than the steel tube. **Note:** We need to always remember that the sound waves cannot travel through the vacuum and the speed of the sound wave propagation is dependent on the medium in which it travels. We observe this technique in various aspects of our everyday life.