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en/12.1.5.md
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| ### 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. | |||
| @@ -4,7 +4,7 @@Statement | |||
| ### Solution | |||
| − |  | ||
| #### Answer | |||
| 1) $E=2E_0;$ | |||
| 2) $\langle w \rangle = \frac{1}{2\pi} E_0^2 \cos^2 \left( \left( t - \frac{{z}}{2} \right) \frac{\Delta}{2} + \varphi \right).$ | |||
| unchanged lines 5 | |||
| ### Statement | ### 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. | $12.1.5.$ 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. | ||
| @@ -4,7 +4,7 @@Statement | |||
| ### Solution | ### Solution | ||
|  | ||
| #### Answer | #### Answer | ||
| 1) $E=2E_0;$ | 1) $E=2E_0;$ | ||
| 2) $\langle w \rangle = \frac{1}{2\pi} E_0^2 \cos^2 \left( \left( t - \frac{{z}}{2} \right) \frac{\Delta}{2} + \varphi \right).$ | 2) $\langle w \rangle = \frac{1}{2\pi} E_0^2 \cos^2 \left( \left( t - \frac{{z}}{2} \right) \frac{\Delta}{2} + \varphi \right).$ | ||
| unchanged lines 5 | |||