The Mach number M of an airplane is the ratio of its speed to the speed of sound. When
Chapter 6, Problem 126(choose chapter or problem)
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
\(\sin \frac{\theta}{2}=\frac{1}{M}\).
(a) Find the angle \(\theta\) that corresponds to a Mach number of 1.
(b) Find the angle \(\theta\) that corresponds to a Mach number of 4.5.
(c) The speed of sound is about 760 miles per hour. Determine the speed of an object having the Mach numbers in parts (a) and (b).
(d) Rewrite the equation as a trigonometric function of \(\theta\).
Text Transcription:
theta
sin theta/2 = 1/M
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