Concept explainers
(a)
Time at which signal will be received at
(a)
Answer to Problem 17P
At
Explanation of Solution
Formula used:
The equation of wave fronts observed in system K at time t at x, y, and z.
Where, x, y, z are the coordinates of the t, is the time and c is the velocity of the light.
Calculation:
Here given data are as follows:
Substituting the value of the coordinates and time in equation
After further simplification,
Conclusion:
Therefore, time taken by the signal to reach at
(b)
The coordinates of the system Kʹ at time
(b)
Answer to Problem 17P
Coordinates of the system Kʹ at time
Explanation of Solution
Formula used:
With the use of the Lorentz transformation equations:
Where, x, y, and z are the coordinates of the system K at time t, v is the speed of the system Kʹ and
Where γ is relativistic factor which can be obtained by the formula:
Calculation:
The motion of the system Kʹ is only along x- direction, therefore,
Now, from equation (I), (II), and (III) calculate value of xʹ and tʹ by substituting the values of x, t, v, and
Now calculate the value of the tʹ
After further simplification
Conclusion:
Therefore, the coordinates of the system Kʹ at time
(c)
(c)
Answer to Problem 17P
The speed of the light in the system Kʹ
Explanation of Solution
The equation of wave fronts observed in system Kʹ at time tʹ at xʹ, yʹ, and zʹ.
Where, xʹ, yʹ, and zʹ are the coordinates of the system Kʹ, tʹ, is the time and cʹ is the velocity of the light measured in system Kʹ.
Calculation:
Substitute the values
Which is almost equal to
Conclusion:
Therefore, speed of the light in both system is
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Chapter 2 Solutions
Modern Physics for Scientists and Engineers
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