Sound travels at different speeds in gases depending on their temperature and density.
The equation relating the speed of sound in a gas to its density is:
speed of sound=Kdensitywhere K is a constant. \text{speed of sound} = \frac{K}{\sqrt{\text{density}}} \quad \text{where } K \text{ is a constant.} speed of sound=densityKwhere K is a constant.The table below shows some data for carbon dioxide gas at two different temperatures.
| Temperature | Speed of sound in m/s | Density of carbon dioxide in kg/m3^33 |
|---|---|---|
| At 0∘C0^\circ\text{C}0∘C | 259 | 1.98 |
| At 100∘C100^\circ\text{C}100∘C | 1.45 |
Use the equation and the data in the table to calculate the speed of sound in carbon dioxide at 100∘C100^\circ\text{C}100∘C.
Give your answer to an appropriate number of significant figures.