Chapter 12, Problem 59P

(a)

To determine

To calculate:The speed of an object moving on land.

Answer to Problem 59P

The speed of an object moving on land is $v_o=113.2\text{ m/s}$ .

Explanation of Solution

Given:

Mach number $\left(M\right)$ $=0.33$

Temperature $\left(T\right)$ $=20°\text{C}$

Formula used:

Mach number is defined as the ratio of speed of an object to the speed of sound in surrounding medium.

Mathematically,

  $M=\frac{v_o}{C}$

  $M=$ Mach number, no units

  $v_o=$ velocity of an object, m/s

  $C$ =velocity of sound in vacuum, m/s

Calculation:

Speed of sound, $C$ at $20°\text{C}$ is $343\text{ m/s}.$

Substitute the values in the equation,

  $0.33=\frac{v_o}{343\text{ m/s}}$

  $v_o=113.2\text{ m/s}$ .

Conclusion:

The speed of an object moving on land is $v_o=113.2\text{ m/s}$ .

(b)

To determine

To calculate: The speed of sound at the altitude.

Answer to Problem 59P

The speed of sound at the altitude $C=260.4\text{ m/s}$ .

Explanation of Solution

Given:

Speed of jet $\left(v_{jet}\right)$ $=3000\text{ km/h}$ $=3000\times \frac{5}{18}\text{ m/s}$ $=833.33\text{ m/s}.$

Mach number $\left(M\right)$ = 3.2

Formula used:

  $M=\frac{v_{jet}}{C}$

  $v_{jet}=$ jet velocity, m/s

Calculation:

Substituting the values,

  $3.2=\frac{833.3\text{ m/s}}{C}$

  $C=260.4\text{ m/s}$

Conclusion:

The speed of sound at the altitude $260.4\text{ m/s}.$