condition of destructive interference:
Δr=(2m−1)2λ
Δr=∣PA−PB∣
By the condition of the problem
Point P is located somewhere between A and B:
PA+PB=AB;AB=16
PB=AB−PA
∣PA−PB∣=∣PA−(AB−PA)∣=∣2∗PA−AB∣=
∣−(AB−2∗PA)∣=∣AB−2∗PA∣=∣16−2∗PA∣
λ=4cm
then condition of destructive interference:
∣16−2∗PA∣=2∗(2m−1);m∈Z;
∣16−2∗PA∣=4m−2;m∈Z;(1)
A.PA=7
condition(1) true
∣16−14∣=4m−2 for m=1
B.PA=8
Δr=∣16−2∗PA∣=16−16=0
0=4m−2
m=21;m∈/Z
condition(1) false
C.PA=9
condition(1) true
∣16−18∣=4m−2 for m=1
D.PA=11
condition(1) true
∣16−22∣=4m−2 for m=2
Answer:A,C,D
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