Air temperature in the Sahara Desert can reach 56.0 degrees Celsius. What is the speed of sound in air that is of this temperature?
In this problem, we’ll assume that the speed of sound in air at a temperature of zero degrees Celsius is exactly 331.5 meters per second. We know that the speed of sound in air changes as a function of air temperature. And in particular, that speed is given by an equation which states that the speed of sound in air 𝑉 is equal to the speed of sound in air when the temperature is zero degrees Celsius multiplied by the square root of one plus the fraction 𝑡, where 𝑡 is the temperature of the air in degrees Celsius, divided by 273 degrees Celsius.
In addition to this equation, we know that the speed of sound in air that is at zero degrees Celsius, we’ve said equal to exactly 331.5 meters per second. When we apply this relationship to our situation, we see that we can use the value for the speed of sound in air at zero degrees Celsius as well as the given air temperature in the problem statement, 56.0 degrees Celsius.
When we enter these values into this equation and then enter in these values on a calculator, we find that the speed of sound in air that is at 56.0 degrees Celsius, to three significant figures, is equal to 364 meters a second.
So we see that sound moving through air at warmer temperatures travels faster.