Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 11 - Oscillations and Waves - Questions: 19

Answer

The wave with the shorter wavelength transmits more energy by a factor of 4.

Work Step by Step

The waves have the same speed v. The wave speed is related to the frequency and wavelength by $v=f \lambda$ so the wave with half the wavelength as the other has twice the frequency. From equation 11–18 we see wave intensity is proportional to the square of the frequency f. The wave with the shorter wavelength has 4 times the intensity as the other wave, i.e., transmits four times the energy in the same time interval.
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