Essential University Physics: Volume 1 (3rd Edition)

Published by Pearson
ISBN 10: 0321993721
ISBN 13: 978-0-32199-372-4

Chapter 14 - Exercises and Problems: 76

Answer

The proof is below.

Work Step by Step

Normally, the period would be how fast the wave approaches you, which is: $T = \frac{\lambda}{v}$ However, now you are also moving at speed u in the direction of the wave, so we add this velocity to obtain: $T' = \frac{\lambda}{v+u}$ We are now asked to show that this can be changed to be like equation 14.16. Thus, using the fact that the period is the inverse of the frequency and substitution, we find: $f'= \frac{v+u}{\lambda}$ $f'= (\frac{v}{\lambda})(1+\frac{u}{v})$ $f'= (f)(1+\frac{u}{v})$ Thus, the proof is complete.
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