Question

Show that the speed of sound in $\mathbf{20}\mathbf{.}{\mathbf{0}}^{\mathbf{\circ }}\mathit{C}$air is 343 m/s , as claimed in the text.

Short answer

The speed is343 m/s

Step-by-step solution

Given Data

The temperature is,

$$\begin{gathered} T=20.0^{\circ }C \\ =\left(273+20.0\right)K \\ =293K \end{gathered}$$

Given Data

the speed of the sound wave increases proportionally with the increase in the temperature of the gas. Thus, the higher the temperature of the gas, higher the velocity of sound in it.

Calculation of the speed

The speed of a wave is given by,

$\frac{v}{V}=\sqrt{\frac{T}{273}}$

For, V = 331 m/s the speed of sound in air at 273 K, we get

$$\begin{gathered} v=\left(331m/s\right)\sqrt{\frac{293K}{273K}} \\ =343m/s \end{gathered}$$

The speed of sound is the same as the speed mentioned in the question.