Question

FIGURE EX17.15 shows a standing sound wave in an 80-cm-long tube. The tube is filled with an unknown gas. What is the speed of sound in this gas?

Short answer

The speed of sound in the gas is$400m/s$.

Step-by-step solution

Given information

A standing sound wave in an 80-cm-long tube is shown below

Speed of sound in gas

At the ends of the tube, the gas molecules exhibit maximum displacement, resulting in antinodes at the ends.

There is another antinode in the middle of the tube.

Thus, this is the $m=2$mode and the wavelength of the standing wave is equal to the length of the tube, that is, $\lambda =0.80m$

The relation between wavelength, frequency, and speed of the wave is given by $v=f\lambda$.

Substitute the given values

$$\begin{gathered} v=500\times 0.80 \\ =400m/s \end{gathered}$$

Therefore, the speed of sound in the gas is$400m/s$.