You've entered the Great Space Race. Your engines are hearty enough to keep you in second place. While racing, the person in front of you begins to have engine troubles and turns on his emergency lights that emit at a frequency of 5.900x10¹⁴ Hz.
If the person in front of you is traveling 2616 km/s faster than you when he turns on his lights, what is the frequency of the emergency lights that you observe when it reaches you in your spaceship?

Explanation:

We shall apply the formula of red shift in radiation when a source of light moves away from the earth . Change in wavelength and velocity of source are related by the following formula .

Δλ / λ = v / c , Δλ is change in wavelength of source radiation ,  λ is original wavelength , v is velocity of source and c is velocity of light .

Δλ  in this case is positive as source is going away .

v = 2616 x 10³ m /s , c = 3 x10⁸ m /s

λ  = 3 x 10⁸ / 5.9 x 10¹⁴ = .50847 x 10⁻⁶ m

Δλ / λ = v / c

Δλ / .50847 x 10⁻⁶ = 2616 x 10³ /  3 x10⁸

Δλ / .50847 x 10⁻⁶ = 872 x 10⁻⁵

Δλ  = .50847 x 10⁻⁶ x  872 x 10⁻⁵

= 443.385 x 10⁻¹¹

= .00443385 x 10⁻⁶

apparent wavelength = λ +Δλ

= .50847 x 10⁻⁶ + .00443385 x 10⁻⁶

= .51290385 x 10⁻⁶

apparent frequency = 3 x 10⁸ / .51290385 x 10⁻⁶

= 5.85 x 10¹⁴ Hz.