How fast one must move to see a red light signal as a green one? (Take, f$_{R}$ = 4.8 × 10$^{14}$ Hz and f$_{G}$ = 5.6 × 10$^{14}$ Hz)

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Aicharya · Accepted Answer

Sol. As, we know, $f' = f\left(\frac{1+(v/c)}{1-(v/c)}ight)^{1/2}$ ∴ $5.6	imes10^{14} = 4.8	imes10^{14}\left(\frac{1+(v/c)}{1-(v/c)}ight)^{1/2}$ $\Rightarrow \frac{7}{6} = \left(\frac{1+(v/c)}{1-(v/c)}ight)^{1/2} \Rightarrow \frac{49}{36} = \frac{1+(v/c)}{1-(v/c)}$ $\Rightarrow 49 - 49\left(\frac{v}{c}ight) = 36 + 36\left(\frac{v}{c}ight) \Rightarrow 85\left(\frac{v}{c}ight) = 13$ $\Rightarrow v = \frac{13}{85}	imes 3	imes10^{8} = \frac{39}{85}	imes10^{8} = 4.59	imes10^{7}$ ms$^{-1}$ Answer: $4.59 	imes 10^7$ ms$^{-1}$

How fast one must move to see a red light signal as a green one? (Take, f$_{R}$ = 4.8 × 10$^{14}$ Hz and…

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