Question

What is the speed of sound in air when the temperature is $20{}^\circ C$?

Answer 1

Hint: We know that the speed of sound could be defined as the distance travelled by a sound wave per unit time when it is propagating through some elastic medium. One could first recall the value of this speed of sound wave at $0{}^\circ C$ and then you may recall the relation for finding the speed of sound at a particular temperature. You may then do the substitutions accordingly to get the answer.

Formula used:
Speed of sound in air at$T{}^\circ C$,
${{c}_{air}}\left( T \right)=331.3\sqrt{1+\dfrac{T}{273.15}}m{{s}^{-1}}$

Complete step-by-step solution:
In the question, we are asked to give the speed of sound in air when the temperature of the air is$20{}^\circ C$.
You may recall that the speed of sound in dry air at $0{}^\circ C$ that is, 273.15K is$331.3m{{s}^{-1}}$. For a temperature of$T{}^\circ C$, the speed of sound in air could be given by the following expression,
${{c}_{air}}\left( T \right)=331.3\sqrt{1+\dfrac{T}{273.15}}m{{s}^{-1}}$
Now, in the question, we are asked to find the speed of sound in air at$20{}^\circ C$. So, on substituting the values into the above relation we get,
${{c}_{air}}\left( 20 \right)=331.3\sqrt{1+\dfrac{20}{273.15}}m{{s}^{-1}}$
$\therefore {{c}_{air}}\left( 20{}^\circ C \right)=343.2m{{s}^{-1}}$
Therefore, we found that the speed of sound in dry air at a temperature $20{}^\circ C$ would be$343.2m{{s}^{-1}}$ .

 Note: The two main factors on which the speed of the sound waves depends are the temperature and composition of the medium. It also does have a weak dependence on the frequency and pressure for the case of ordinary air. Also, this value of speed of sound also varies from substance to substance.