The Mach Number M of an Airplane Is the Ratio $\theta$

question 68

Multiple Choice

The mach number M of an airplane is the ratio of its speed to the speed of sound.When an airplane travels faster than the speed of sound, the sound waves form a cone behind the airplane (see figure) .The mach number is related to the apex angle $\theta$ of the cone by $\sin ( \theta / 5 ) = 1 / M$ .
Rewrite the equation in terms of $\theta$ .

• A) \(\theta = 5 \sin \left( \frac { 1 } { M } \right)\)
• B) \(\theta = \sin \left( \frac { 1 } { M } \right)\)
• C) \(\theta = \sin ^ { - 1 } \left( \frac { 1 } { M } \right)\)
• D) \(\theta = 5 \sin ^ { - 1 } \left( \frac { 5 } { M } \right)\)
• E) \(\theta = 5 \sin ^ { - 1 } \left( \frac { 1 } { M } \right)\)

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