Concept explainers
The wave intensity at a distance
Answer to Problem 73CP
It is proved that the wave intensity at a distance
Explanation of Solution
The wave front that passes the observer is spherical. Consider
Write the expression for average power.
The radius of the wave front received by the observer at a distance
Here,
The forward distance travelled by the source due to the radiation form the source.
Here,
The total distance traveled by the wave front is the sum of the distance
Write the expression for the total distance traveled by the wave front, and obtain an expression for
The energy per unit area during one cycle gives the intensity of the wave.
Write the expression for the intensity of the wave.
Here,
Write the expression for the area of a spherical wave front.
Substitute,
Substitute,
Write an expression for the time taken by the wave front to pass the observer.
Here,
Write the expression for the Doppler shifted frequency.
The intensity of the wave received by the observer is.
Substitute,
Conclusion:
Therefore, it is proved that the wave intensity at a distance
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Chapter 17 Solutions
Physics for Scientists and Engineers with Modern Physics, Technology Update
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