Conceptual Physics (12th Edition)

Published by Addison-Wesley
ISBN 10: 0321909100
ISBN 13: 978-0-32190-910-7

Chapter 19 - Think and Solve - Page 370: 40


The plane is traveling at 1.41 times the speed of sound (aka Mach 1.41).

Work Step by Step

In the same time that it takes sound to travel from point A to point C, the plane has moved from point A to point B. Triangle ACB is a special 45-45-90 right triangle. The distance traveled by the plane, AB, is $\sqrt{2} \times AC$. An internet search for the term "Mach angle" shows that generally, the sine of the half-angle gives the ratio of the speed of sound to the speed of the plane. $$sin(45^{\circ}) = \frac{1}{\sqrt{2} } = \frac{v_{sound}}{v_{plane}}$$ This gives the same answer.
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