Concept explainers
(a)
The resultant intensity when the waves interfere constructively.
(a)
Answer to Problem 93P
The resultant intensity when the waves interfere constructively is
Explanation of Solution
Given that the amplitudes of the interfering waves are
Write the expression for the intensity of the EM wave.
Here,
Write the expression for the average energy density of the wave.
Here,
Write the expression for the rms amplitude of the wave.
Here,
Use equation (III) in (II).
Use equation (IV) in (I).
Write the expression for the resultant amplitude when two EM waves undergo constructive interference.
Conclusion:
Substitute
Substitute
Therefore, the resultant intensity when the waves interfere constructively is
(b)
The resultant intensity when the waves interfere destructively.
(b)
Answer to Problem 93P
The resultant intensity when the waves interfere destructively is
Explanation of Solution
Given that the amplitudes of the interfering waves are
Write the expression for the resultant amplitude when two EM waves undergo destructive interference.
Equation (V) fives the resultant intensity of the wave.
Conclusion:
Substitute
Substitute
Therefore, the resultant intensity when the waves interfere destructively is
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