Chapter 11, Problem 15Q

To determine

The wave which transmits more energy and by what factor.

Answer to Problem 15Q

Solution:

The wave with a shorter wavelength transmits twice the energy of the other wave.

Explanation of Solution

The energy transmitted by the wave:

  $E\propto \frac{1}{\lambda }$

Let ${\lambda }_1\text{and}{\lambda }_2$ be the wavelengths of the two linear waves.

Given, ${\lambda }_2=\frac{{\lambda }_1}{2}$

Hence,

  $\begin{array}{l}\frac{E_1}{E_2}=\frac{{\lambda }_2}{{\lambda }_1}=\frac{1}{2}\\ \Rightarrow E_2=2E_1\end{array}$

Hence, the wave with a shorter wavelength has higher energy $E_2>E_1$ .

Conclusion:

The wave with the shorter wavelength would transmit two times the energy transmitted by the other wave.