Two starships, the Enterprise and the Constitution, are approaching each other head-on from a great distance. The separation between them is decreasing at a rate of 713.0 km/s. The Enterprise sends a laser signal toward the Constitution. If the Constitution observes a wavelength? = 712.2 nm, what wavelength was emitted by the Enterprise? Express your answer with four significant digits.

Question

Physics

Kendall Cook

24 September, 10:19

Two starships, the Enterprise and the Constitution, are approaching each other head-on from a great distance. The separation between them is decreasing at a rate of 713.0 km/s. The Enterprise sends a laser signal toward the Constitution. If the Constitution observes a wavelength? = 712.2 nm, what wavelength was emitted by the Enterprise? Express your answer with four significant digits.

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Answers (1)

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Gideon Cox · Answer 1

Assume the enterprise is sitting with zero velocity, while the Constitution is moving towards the enterprise at a speed of 713km/s

V = 713,000 m/s

Since the constitution is moving into the wave, then it will be compressed.

So, we want to find the original wavelength λ

So using relativity formula

λ' = λ (c+Vo) / (c + V)

Given that,

λ' = 712.2nm = 712.2 * 10^-9m

c = 3*10^8 m/s

Vo = 0

V = 713,000 m/s

Then,

λ' = λ (c+Vo) / (c + V)

712.2 * 10^-9 = λ (3*10^8+0) / (3*10^8+713,000)

712.2*10^-9=λ (3*10^8) / (3.00713*10^8)

712.2*10^-9=λ * 0.9976

λ = 712.2 * 10^-9 / 0.9976

λ = 713.9 * 10^-9

λ = 713.9 nm

Which is a bit longer as expected