The Mach number indicates how many times a speed is greater than the speed of sound.
So, to find the Mach number, we just need to divide the speed by the speed of sound.
a) at 30°C, the speed of sound is 349 m/s, so we have:
[tex]\frac{332}{349}=0.95[/tex]b) at -10°C, the speed of sound is 325 m/s, so we have:
[tex]\frac{340}{325}=1.05[/tex]c) at 13°C, the speed of sound is 339 m/s. First, let's convert the speed from km/h to m/s:
[tex]\begin{gathered} 6000\text{ km/h}=\frac{6000}{3.6}\text{ m/s}=1666.67\text{ m/s} \\ \frac{1666.67}{339}=4.92 \end{gathered}[/tex]d) at -13°C, the speed of sound is 323 m/s, so we have:
[tex]\frac{1666.67}{323}=5.16[/tex]