Chapter 15, Problem 82A

To determine

To calculate: Speed of sound at $57°\text{C}$ and $-62°\text{C}$ .

Answer to Problem 82A

Speed of sound at $57°\text{C}$ is $\underset{\_}{365.2\text{ m/s}}$ .

Speed of sound at $-62°\text{C}$ is $\underset{\_}{\text{293}\text{.8 m/s}}$ .

Explanation of Solution

Given:

The following temperatures:

$57°\text{C}$ and $-62°\text{C}$

Calculation:

The speed of sound in air at $20°\text{C}$ is $\text{343 m/s}$ .

The speed of sound increases by $\text{0}\text{.6 m/s}$ for every $1°\text{C}$ rise in temperature.

For $57°\text{C}$ , temperature increases by $\text{57}-\text{20=37}°\text{C}$ . Speed of sound will increase by $\text{0}\text{.6}\times \text{37=22}\text{.2 m/s}$ .

Therefore, speed of sound at $57°\text{C}$ = $343+22.2=365.2\text{ m/s}$

For $-62°\text{C}$ , temperature decreases by $-62-\text{20=}-\text{82}°\text{C}$ . Speed of sound will decrease by $\text{0}\text{.6}\times -82\text{=}-49.2\text{ m/s}$ .

Therefore, speed of sound at $-62°\text{C}$ = $343-49.2=293.8\text{ m/s}$

Conclusion:

Speed of sound at $57°\text{C}$ is $\underset{\_}{365.2\text{ m/s}}$ .

Speed of sound at $-62°\text{C}$ is $\underset{\_}{\text{293}\text{.8 m/s}}$ .