Explanation Given info: The distant between the Enterprise and the Constitution is decreasing at the rate of 782.5 km / s and the wavelength observed by the constitution is 670.3 nm . From the Doppler’s effect the observed frequency of a moving source is, f ′ = f ( 1 ± u c ) The separation between two stars is decreasing and so the observed frequency increase and the sign of u is positive. The above equation becomes, f ′ = f ( 1 + u c ) (1) Here, c is the speed of light . u is the speed of the star. f is the frequency emitted by the star. The speed of electromagnetic wave is, c = f λ Here, λ is the wavelength of electromagnetic wave. f is the frequency of electromagnetic wave. Solve the above equation for f . f = c λ Substitute c λ for f and c λ ′ for f ′ in equation (1). c λ ′ = c λ ( 1 + u c ) 1 λ ′ = 1 λ ( 1 + u c ) λ = λ ′ ( 1 + u c ) Substitute 3 × 10 8 m / s for c , 782

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Chapter 25, Problem 21PCE

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The wavelength emitted by the Enterprise.

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Chapter 25, Problem 20PCE

Chapter 25, Problem 22PCE

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The wavelength emitted by the Enterprise.

Solution Summary: The author explains that the distance between the Enterprise and the Constitution is decreasing at the rate of 782.5. The Doppler’s effect the observed frequency of a moving source is positive.

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