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Solved: Recall, from this chapter, that the factor gamma
Chapter 17, Problem 1P(choose chapter or problem)
Recall, from this chapter, that the factor gamma (?) governs both time dilation and length contraction, where ? When you multiply the time in a moving frame by ?, you get the longer (dilated) time in your fixed fame. When you divide the length in a moving frame by ?, you get the shorter (contracted) length in your fixed frame. Consider a high-speed rocket ship equipped with a flashing light source. If the frequency of flashes seen on an approaching ship is twice what it was when the ship was a fixed distance away, by how much is the period (time interval between flashes) changed? Is this period constant for a constant relative speed? For accelerated motion? Defend your answer.
Questions & Answers
QUESTION:
Recall, from this chapter, that the factor gamma (?) governs both time dilation and length contraction, where ? When you multiply the time in a moving frame by ?, you get the longer (dilated) time in your fixed fame. When you divide the length in a moving frame by ?, you get the shorter (contracted) length in your fixed frame. Consider a high-speed rocket ship equipped with a flashing light source. If the frequency of flashes seen on an approaching ship is twice what it was when the ship was a fixed distance away, by how much is the period (time interval between flashes) changed? Is this period constant for a constant relative speed? For accelerated motion? Defend your answer.
ANSWER:Solution 1P Step 1: Consider the frequency of the flashlight as “f” when the ship was at fixed distance away. Suppose, the time taken by the flashlight to reach the approaching ship will be “T” if the ships are at fixed distance. So, the time period of flashlight is “T”. If the ship with flashlight started to move, provided that the frequency recorded at the approaching ship is doubled that is, “2f”. So, we know that, the frequency and time is related as, f 1/ T (in the first case).----------- (1) So, we have to calculate the new time period for the flashlight if the frequency while moving is recorded as “2f”. So, we can write, 2 f 1/ T ‘ ------------ (2) Divide equation (2) by (1) we get, (2f / f) = (1 / T ‘ ) /(1/ T) Or, 2 = T / T ‘ 2T ‘ = T Or T ‘ = T /2 So, the time period of flashlight will get halved as the frequency is getting doubled due to the relative motion of the spaceship.