Question

Show that the speed of sound in $20^\circ\textrm{C}$ air is 343 m/s, as claimed in the text.

Final Answer

see explanation in the video.

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Video Transcript

This is College Physics Answers with Shaun Dychko.
We are going to show that the speed of sound in air that has a temperature of 20 degrees Celsius is 343 meters per second. So we have a formula for the speed of sound based on the air temperature which is 331 meters per second multiplied by the square root of the air temperature divided by 273 Kelvin. So this temperature in the numerator of this fraction has to be absolute temperature. So we need to convert the 20 degrees Celsius into Kelvin by adding 273.15. And so we go 331 times square root of 20 plus 273.15 divided by 273 giving us 343 meter per second. And so we have verified that this is indeed the speed when the air temperature is 20 degrees Celsius.