Edits to “Statement”, “Solution”, “Answer”
en/12.1.5.md
+6 −3
| @@ -1,13 +1,16 @@ | |||
| ### Statement | |||
| − | $12.1.5.$ [Insert the problem statement] | ||
| + | $12.1.5.$ Two plane sinusoidal waves, each with amplitude $E_0$, have frequencies ω and $\omega + \Delta$, respectively, where $\Delta < \omega$, and propagate in the same direction, superimposing on each other. What is the maximum amplitude of the resultant wave? Determine the distribution of the average energy density of the resultant wave along the direction of propagation. | ||
| ### Solution | |||
| − |  | ||
| #### Answer | |||
| − | [Insert a concise answer or boxed result] | ||
| + | 1) $E=2E_0;$ | ||
| + | |||
| + | 2) | ||
| + | $\langle w \rangle = \frac{1}{2\pi} E_0^2 \cos^2 \left( \left( t - \frac{{z}}{2} \right) \frac{\Delta}{2} + \varphi \right).$ | ||
| @@ -1,13 +1,16 @@ | |||
| ### Statement | ### Statement | ||
| $12.1.5.$ [Insert the problem statement] | $12.1.5.$ Two plane sinusoidal waves, each with amplitude $E_0$, have frequencies ω and $\omega + \Delta$, respectively, where $\Delta < \omega$, and propagate in the same direction, superimposing on each other. What is the maximum amplitude of the resultant wave? Determine the distribution of the average energy density of the resultant wave along the direction of propagation. | ||
| ### Solution | ### Solution | ||
|  | ||
| #### Answer | #### Answer | ||
| [Insert a concise answer or boxed result] | 1) $E=2E_0;$ | ||
| 2) | |||
| $\langle w \rangle = \frac{1}{2\pi} E_0^2 \cos^2 \left( \left( t - \frac{{z}}{2} \right) \frac{\Delta}{2} + \varphi \right).$ | |||