Physics Technology Update (4th Edition)

Published by Pearson
ISBN 10: 0-32190-308-0
ISBN 13: 978-0-32190-308-2

Chapter 14 - Waves and Sound - Problems and Conceptual Exercises - Page 493: 43

Answer

$\lambda_3\lt \lambda_2\lt \lambda_1$

Work Step by Step

According to Doppler's effect $f_{\circ}=f_s[\frac{1+(\frac{v_{\circ}}{v})}{1-(\frac{v_s}{v})}]$...eq(1) We plug in the known values to obtain: $f_2=f_1[\frac{1+\frac{0}{v}}{1-\frac{u}{v}}]$ $\implies f_2=\frac{f_1}{1-\frac{u}{v}}$ As $u\lt v$ $\implies 0\lt 1-\frac{u}{v}\lt 1$ Thus, $f_2\gt f_1$ Now plug in $u$ for $v_{\circ}$, $0$ for $v_s$ and $f_2$ for $f_s$ in eq(1) to obtain: $f_3=f_2[\frac{1+(\frac{u}{v})}{1-(\frac{0}{v})}]$ $f_3=(1+\frac{u}{v})f_2$ This shows that $f_3\gt f_2$ Thus, $f_3\gt f_2\gt f_1$ As frequency is inversely proportional to the wavelength, therefore the order of the wavelength is $\lambda_3\lt \lambda_2\lt \lambda_1$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.