(a)
The time elapse between the emission of wavefronts by the source, in observer’s frame.
(a)

Answer to Problem 96P
The time elapse between the emission of wavefronts by the source, in observer’s frame is
Explanation of Solution
Write the expression for the proper time interval.
Here,
Write the expression for the period of the wavefront emission.
Here,
Use equation (II) in (I).
Write the expression for the time elapse between the emission of wavefronts by the source, in observer’s frame.
Here,
Write the expression for the time interval corresponding to the proper time interval, in observer’s frame.
Here,
Use equation (III) in (V).
Use equation (VI) in (IV).
Conclusion:
Therefore, the time elapse between the emission of wavefronts by the source, in observer’s frame is
(b)
The time
(b)

Answer to Problem 96P
The time
Explanation of Solution
Write the expression for the time that the first wavefront described in the problem statement arrives at the observer.
Here,
Write the expression for the time of travel of the second wavefront as it arrives at the observer.
Here,
Write the expression for time
Use equation (VIII) and (IX) in (X).
Use equation (VII) in (XI).
Conclusion:
Therefore, the time
(c)
To show that the frequency detected by the observer is
(c)

Answer to Problem 96P
The frequency detected by the observer is
Explanation of Solution
Write the expression for the frequency detected by the observer.
Use equation (XII) in (XIII).
Write the expression of Lorentz constant.
Use equation (XV) in (XIV) and simplify.
Conclusion:
Therefore, the frequency detected by the observer is
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Chapter 26 Solutions
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