Chapter 8, Problem 8.1P

Consider air at a temperature of 230 K. Calculate the speed of sound.

To determine

The speed of sound.

Answer to Problem 8.1P

The speed of sound is $v=303.996\text{m}/\text{s}$ .

Explanation of Solution

Given:

The temperature of air is $T=230\text{K}$ .

Formula used:

The expression for speed of sound is given as,

  $v=\sqrt{\gamma RT}$

Here, $\gamma$ is the specific heat ratio for the air and $R$ is the gas constant for air.

Calculation:

The value of $\gamma$ for air is $1.4$ and the value of $R$ is $287\text{J}/\text{kg}\cdot \text{K}$ .

The speed of sound can be calculated as,

  $\begin{array}{l}v=\sqrt{\gamma RT}\\ v=\sqrt{1.4\times 287\text{J}/\text{kg}\cdot \text{K}\left(\frac{\text{1}\frac{\text{kg}\cdot {\text{m}}^{\text{2}}}{{\text{s}}^{\text{2}}}}{1\text{J}}\right)\times 230\text{K}}\\ v=303.996\text{m}/\text{s}\end{array}$

Conclusion:

Therefore, the speed of sound is $v=303.996\text{m}/\text{s}$ .