Ta có công thức:
$\lambda =2\pi c\sqrt{LC}$
$\to {{\lambda }^{2}}$$\sim$$C$
$\to$ chỗ nào có $C$, ta thay bằng ${{\lambda }^{2}}$
Tính ${{\lambda }_{3}};{{\lambda }_{4}}$
${{\lambda }_{3}}=\dfrac{c}{{{f}_{3}}}=\dfrac{{{3.10}^{8}}}{2,4\,.\,{{10}^{6}}}=125\,\,\left( m \right)$
${{\lambda }_{4}}=\dfrac{c}{{{f}_{4}}}=\dfrac{3\,.\,{{10}^{8}}}{5\,.\,{{10}^{6}}}=60\,\,\left( m \right)$
Ta có:
$\,\,\,\,\,\,{{C}_{3}}={{C}_{1}}+{{C}_{2}}$
$\to {{\lambda }_{3}}^{2}={{\lambda }_{1}}^{2}+{{\lambda }_{2}}^{2}$
$\to {{125}^{2}}={{\lambda }_{1}}^{2}+{{\lambda }_{2}}^{2}$
$\to {{\lambda }_{1}}^{2}+{{\lambda }_{2}}^{2}=15625$
$\,\,\,\,\,\,{{C}_{4}}=\dfrac{{{C}_{1}}\,.\,{{C}_{2}}}{{{C}_{1}}+{{C}_{2}}}$
$\to {{\lambda }_{4}}^{2}=\dfrac{{{\lambda }_{1}}^{2}\,.\,{{\lambda }_{2}}^{2}}{{{\lambda }_{1}}^{2}\,+\,{{\lambda }_{2}}^{2}}$
$\to {{60}^{2}}=\dfrac{{{\lambda }_{1}}^{2}\,.\,{{\lambda }_{2}}^{2}}{15625}$
$\to {{\lambda }_{1}}^{2}.{{\lambda }_{2}}^{2}=56250000$
Ta có hệ như sau:
$\begin{cases} {{\lambda }_{1}}^{2}+{{\lambda }_{2}}^{2}=15625\\\\ {{\lambda }_{1}}^{2}.{{\lambda }_{2}}^{2}=56250000\end{cases}$
Theo Vi – et đảo, ${{\lambda }_{1}}^{2}\,;\,{{\lambda }_{2}}^{2}$ là nghiệm của phương trình:
${{X}^{2}}-15625X+56250000=0$
$\to X=10000$ hoặc $X=5625$
$\to\begin{cases}\lambda_1^2=10000\\\\\lambda_2^2=5625\end{cases}$ hoặc $\begin{cases}\lambda_1^2=5625\\\\\lambda_2^2=10000\end{cases}$
$\to\begin{cases}\lambda_1=100\,\,\left(m\right)\\\\\lambda_2=75\,\,\left(m\right)\end{cases}$ hoặc $\begin{cases}\lambda_1=75\,\,\left(m\right)\\\\\lambda_2=100\,\,\left(m\right)\end{cases}$
