1. 1 $\left(\omega t_{0}-k(x+\lambda)+\varphi\right)-\left(\omega t_{0}-k x+\varphi\right)=2 \pi$ | 0.20 |
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1. 2 $k=\cfrac{2\pi}{\lambda}$ | 0.20 |
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1. 3 $\left(\omega(t+T)-k x_{0}+\varphi\right)-\left(\omega t-k x_{0}+\varphi\right)=2 \pi$ | 0.20 |
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1. 4 $\omega=\cfrac{2\pi}{T}$ | 0.20 |
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2. 1 $\omega t-kx+\varphi=\mathrm {const}$ | 0.20 |
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2. 2 $v=\cfrac{\omega}{k}$ | 0.20 |
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3. 1 Плоскости, перпендикулярные волновому вектору. | 0.20 |
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4. 1 $E=E_{0}^{\prime} \cos (\omega t-k x \cos \theta-k y \sin \theta+\varphi)$ | 0.20 |
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5. 1 $E=2 E_{0} \cos \left(\left(\omega_{0}+\frac{\Delta \omega}{2}\right) t-\left(k_{0}+\frac{\Delta k}{2}\right) x\right) \cos \left(\frac{\Delta \omega}{2} t-\frac{\Delta k}{2} x\right)$ | 0.20 |
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5. 2 $A_{0}(x, t)=2 E_{0} \cos \left(\cfrac{\Delta \omega}{2} t-\cfrac{\Delta k}{2} x\right)$ | 0.20 |
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6. 1 $\tau=\cfrac{2\pi}{\Delta\omega}$ | 0.20 |
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6. 2 $\tau\Delta\nu=1$ | 0.20 |
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7. 1 $L=\cfrac{2\pi}{\Delta k}$ | 0.20 |
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8. 1 $\omega_0 t-k_0 x=\mathrm{const}$ | 0.20 |
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8. 2 $v_p=\cfrac{\omega_0}{k_0}$ | 0.20 |
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9. 1 $\cfrac{\Delta\omega}{2}t-\cfrac{\Delta k}{2}x=0$ | 0.20 |
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9. 2 $v_g=\cfrac{\Delta\omega}{\Delta k}$ | 0.20 |
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10. 1 $\omega=kc$ | 0.20 |
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10. 2 $v_p=c$ | 0.20 |
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10. 3 $v_g=v_p=c$ | 0.20 |
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11. 1 $k_y=m\cfrac{\pi}{a}$ | 0.20 |
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12. 1 $E_{1}=E_{0}^{\prime} \cos \left(\omega t-k_{0} x \cos \theta+k_{0} y \sin \theta+\varphi\right)$ | 0.30 |
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12. 2 $E_{2}=E_{0}^{\prime} \cos \left(\omega t-k_{0} x \cos \theta-k_{0} y \sin \theta-\varphi\right)$ | 0.30 |
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12. 3 $E_0'=E_0/2$ | 0.20 |
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12. 4 Условие $\varphi=-\pi/2$ | 0.20 |
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13. 1 $k_x=k_0\cos\theta$ | 0.20 |
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13. 2 $k_y=k_0\sin\theta$ | 0.20 |
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14. 1 $\sin\theta_m=m\cfrac{\pi}{ak_0}$ | 0.30 |
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14. 2 $\sin\theta_m=m\cfrac{\lambda}{2a}$ | 0.30 |
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15. 1 $v_p=\cfrac{\omega}{k_0\cos\theta}$ | 0.30 |
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15. 2 $v_{p}=\cfrac{c}{\sqrt{1-\left(m \cfrac{\pi c}{\omega a}\right)^{2}}}$ | 0.30 |
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16. 1 $v_{g}=\cfrac{\Delta \omega}{\Delta k}=\cfrac{d \omega}{d k}=\left(\cfrac{d k}{d \omega}\right)^{-1}$ | 0.30 |
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16. 2 $k=\frac{\omega}{v_{p}}=\cfrac{\omega}{c} \sqrt{1-\left(m \cfrac{\pi c}{\omega a}\right)^{2}}=\cfrac{1}{c} \sqrt{\omega^{2}-\left(m \cfrac{\pi c}{a}\right)^{2}}$ | 0.40 |
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16. 3 $v_{g}=c \sqrt{1-\left(m \cfrac{\pi c}{a \omega}\right)^{2}}$ | 0.30 |
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17. 1 $\sin\theta_m\approx 0.42m$ | 0.20 |
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17. 2 Присутствуют моды с $m=1$ и $m=2$ | 0.30 |
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17. 3 $v=c \sqrt{1-\left(m \cfrac{\lambda}{2 a}\right)^{2}}$ | 0.40 |
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17. 4 $\cfrac{X}{v_1}-\cfrac{X}{v_2}=\tau$ | 0.40 |
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17. 5 $X=1.4c\tau$ | 0.30 |
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18. 1 $\sin\theta_2=2\cfrac{\lambda}{2a} > 1$ | 0.30 |
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18. 2 $\cfrac{a}{\lambda} < 1$ | 0.30 |
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