Wavelength of reflected pulse measured by the first spaceship.
Answer to Problem 54P
Wavelength of reflected pulse will be
Explanation of Solution
Write the equation to find the frequency of pulse received by an observer in first spaceship.
Here,
Write the equation to find the frequency of pulse received by observer in second spaceship.
Here,
Write the relation between
Rewrite the equation for
Rewrite the above equation by substituting the previous equation for
Rewrite the above equation using binomial approximation.
Write the relation between frequency and wavelength of pulse received by observer in second spaceship.
Here,
Write the relation between frequency and wavelength of pulse produced in first spaceship.
Here,
Rewrite equation (I) by substituting equations (II) and (III).
Conclusion:
Substitute
Therefore, the wavelength of reflected pulse will be
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