Question

A radio-controlled model airplane is being flown at 48.3 km/h. if the plane is being flown at Mach 0.040, what is the temperature of the air, to the nearest degree?

Answer 1

By the definition of the Mach number, we have:

$$M=\dfrac{v_{airplane}}{v_{sound}}.$$

Then, we can find the speed of sound in the air:

$$v_{sound}=\dfrac{v_{airplane}}{M},$$ $$v_{sound}=\dfrac{48.3\ \dfrac{km}{h}\times\dfrac{1000\ m}{1\ km}\times\dfrac{1\ h}{3600\ s}}{0.04}=335.4\ \dfrac{m}{s}.$$

Finally, we can find the temperature of the air:

$$v_{sound}=331.3+0.606T,$$ $$T=\dfrac{v_{sound}-331.3}{0.606}=\dfrac{335.4-331.3}{0.606}=7^{\circ}C.$$