I think French wants you to assume that the speed of light depends on the motion of the source. In which case, you cannot use the relativistic Doppler shift, but have to calculate the shift for yourself.ka_reem13 said:
ka_reem13 said:
Chapter 3 of AP French Relativity primarily focuses on the principles of special relativity, including time dilation, length contraction, and the Lorentz transformations. It delves into the implications of these concepts for objects moving at speeds close to the speed of light.
The Lorentz transformation equations are derived by ensuring that the speed of light remains constant in all inertial frames of reference. This involves using the postulates of special relativity and algebraically manipulating the space and time coordinates of events in different inertial frames. The transformations account for the effects of time dilation and length contraction.
Time dilation is the phenomenon where time appears to pass more slowly for an observer in motion relative to a stationary observer. Chapter 3 explains this using the Lorentz transformation equations, showing that the time interval between two events is longer (dilated) when measured in a reference frame moving relative to the events.
Length contraction is the phenomenon where the length of an object moving at relativistic speeds appears shorter along the direction of motion to a stationary observer. Chapter 3 explains this by showing how the Lorentz transformations affect spatial coordinates, leading to a contracted length in the frame of reference moving relative to the object.
Chapter 3 addresses the concept of simultaneity by demonstrating that events that are simultaneous in one frame of reference may not be simultaneous in another frame moving relative to the first. This is a direct consequence of the Lorentz transformations and highlights the relative nature of time in special relativity.