Given:
The speed of the comet, u=255 km/s=255×10³ m/s
The observed frequency, f_o=642×10¹⁴ Hz
To find:
The frequency emitted by the comet.
Explanation:
The observed frequency is given by,
[tex]f_o=\sqrt{\frac{c+u}{c-u}}f[/tex]
Where c is the speed of light and f is the frequency emitted by the comet.
On substituting the known values,
[tex]\begin{gathered} 642\times10^{14}=\sqrt{\frac{3\times10^8+255\times10^3}{3\times10^8-255\times10^3}}\times f \\ \implies f=\frac{642\times10^{14}}{\sqrt{\frac{3\cdot10^{8}+255\cdot10^{3}}{3\cdot10^{8}-255\cdot10^{3}}}} \\ =641\times10^{14}\text{ Hz} \end{gathered}[/tex]
Final answer:
The frequency emitted by the comet is 641×10¹⁴ Hz
