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3 September, 00:26

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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  1. 3 September, 01:18
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    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
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