Consider a high-speed rocket ship equipped with a flashing...

Name: Problem 37, Chapter 35: Conceptual Physics
Uploaded: 2019-09-26T05:10:12-08:00
Duration: 1 min 3 s
Channel: Sri Datta Vikas Buchemmavari
Description: 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.

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.

Key Concepts

Accelerated Motion

With accelerated motion, the relative speed between the source and the observer changes over time. Consequently, the Doppler shift—and thus the observed frequency and period—varies dynamically. This means that while at any specific moment the relationship between frequency and period holds, the value of the period is not constant over time due to the continuous change in acceleration.

Constant Relative Speed

For a constant relative speed, the Doppler shift remains constant, meaning that the observed doubling of frequency (and halving of the period) should persist. In inertial frames with uniform motion, the relative velocity is unchanging, and therefore the frequency and period measured by the observer are steady over time.

Doppler Effect

The Doppler effect describes how the observed frequency of waves (such as light or sound) changes due to the relative motion between the source and the observer. In the context of a high-speed rocket ship, the approaching observer perceives a higher frequency (and therefore a shorter period) of the flashing light due to the motion towards the source.

Frequency and Period Relationship

The frequency of a periodic process is the inverse of its period. When the frequency of flashes doubles, the period between flashes is halved. This simple mathematical relationship is fundamental to understanding oscillatory phenomena in physics, where increasing the rate (frequency) of events necessarily decreases the interval (period) between them.

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