A) 4 : 1
B) 1 : 4
C) 3 : 1
D) 1 : 3
Correct Answer: A
Solution :
The resultant intensity at any point depends upon the phase difference\[\phi \]between the two waves of amplitudes\[{{a}_{1}}\]and\[{{a}_{2}},\]the maximum intensity is given by \[{{I}_{\max }}={{({{a}_{1}}+{{a}_{2}})}^{2}}\] and minimum is given by \[{{I}_{\min }}={{({{a}_{1}}+{{a}_{2}})}^{2}}\] Given, \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{1}{3}\] \[\therefore \] \[{{a}_{1}}=3{{a}_{2}}\] \[{{I}_{\max }}{{(3{{a}_{2}}+{{a}_{2}})}^{2}}={{(4{{a}_{2}})}^{2}}\] \[{{I}_{\min }}{{(3{{a}_{2}}-{{a}_{2}})}^{2}}={{(2{{a}_{2}})}^{2}}\] \[\therefore \] \[\frac{{{I}_{\max }}}{{{I}_{\min }}}=\frac{16}{4}=\frac{4}{1}\]
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