A) \[5\times {{10}^{-7}}m\]
B) \[4\times {{10}^{-9}}m\]
C) \[6\times {{10}^{-7}}m\]
D) \[3\times {{10}^{-6}}m\]
E) None of these
Correct Answer: A
Solution :
Given wave is \[E={{E}_{0}}\sin \,(4\pi \times {{10}^{6}}x-1.2\pi \times {{10}^{15}}t)\] ?(i) But the standard wave equation is \[E={{E}_{0}}\sin \,(Kx-\omega t)\] ?(ii) Comparing Eqs.(i) and (ii), we get \[K=4\pi \times {{10}^{6}}\] \[\Rightarrow \] \[\frac{2\pi }{\lambda }=4\pi \times {{10}^{6}}\] \[\Rightarrow \] \[\lambda =\frac{2\pi }{4\pi \times {{10}^{6}}}=\frac{{{10}^{-6}}}{2}=5\times {{10}^{-7}}m\]
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