Question

A plane polarized monochromatic $EM $ wave is traveling in vacuum along $z$ direction such that at $t = t_1$ it is found that the electric field is zero at a spatial point $z_1$. The next zero that occurs in its neighbourhood is at $z_2$. The frequency of the electromagnetic wave is :

• A. $\frac{3 \times 10^8}{|z_2 - z_1|}$
• B. \(\frac{1.5 \times 10^8}{|z_2 - z_1|}\)
• C. $\frac{6 \times 10^8}{|z_2 - z_1|}$
• D. $\frac{1}{t_1 + \frac{|z_2 - z_1|}{3 \times 10^8}} $

Answer 1

The Correct Option is B

The correct option is(B): \(\frac{1.5 \times 10^8}{|z_2 - z_1|}\)

Since \(c=f \lambda \Rightarrow f=\frac{c}{\lambda}\).
Here, \(\lambda=2\left|z_{2}-z_{1}\right|\) and \(c=3 \times 10^{8} .\) Therefore,
\(f=\frac{3 \times 10^{8}}{2\left|z_{2}-z_{1}\right|}=\frac{1.5 \times 10^{8}}{\left|z_{2}-z_{1}\right|}\)