Question

Calculate the Mach number for the following speeds of sound. State whether the speed issubsonic or supersonic. Assume the speed of sound in air to be 332 m/s:A. 664 m/sB. 306 m/sC. 140 km/hD. 7171 km/h

Answer 1

The Mach number of a speed is given by how many times the speed is greater than the sound speed.

Therefore, to find each Mach number, let's divide the speed by the speed of sound:

A.

`(664)/(332)=2`

So here we have Mach 2. Since the speed is greater than the speed of sound, we have a supersonic sound.

B.

`(306)/(332)=0.92`

Here we have Mach 0.92. Since the speed is smaller than the speed of sound, we have a subsonic sound.

C.

Here we have to convert the given speed to m/s:

`\begin{gathered} 140\text{ km/h}=(140)/(3.6)\text{ m/s}=38.89\text{ m/s} \\ (38.89)/(332)=\text{0}.12 \end{gathered}`

Mach 0.12, subsonic.

D.

`\begin{gathered} 7171\text{ km/h}=(7171)/(3.6)\text{ m/s}=1991.94\text{ m/s} \\ (1991.94)/(332)=6 \end{gathered}`

Mach 6, supersonic.