A) 9 : 1
B) 3:1
C) 2 : 1
D) 1 : 1
Correct Answer: C
Solution :
The intensity depends on phase difference between the two waves. For maximum intensity \[{{I}_{\max }}={{({{a}_{1}}+{{a}_{2}})}^{2}}\] ?. (i) where\[{{a}_{1}}\]and\[{{a}_{2}}\]are the amplitudes of the waves, and minimum intensity is given by \[{{I}_{\min }}={{({{a}_{1}}-{{a}_{2}})}^{2}}\] ? (ii) From Eqs. (i) and (ii), we get \[\frac{{{({{a}_{1}}+{{a}_{2}})}^{2}}}{{{({{a}_{1}}-{{a}_{2}})}^{2}}}=\frac{9}{1}\] Taking square root \[\frac{{{a}_{1}}+{{a}_{2}}}{{{a}_{1}}-{{a}_{2}}}=\frac{3}{1}\] \[\Rightarrow \] \[3{{a}_{1}}-3{{a}_{2}}={{a}_{1}}+{{a}_{2}}\] \[\Rightarrow \] \[2{{a}_{1}}=4{{a}_{2}}\] \[\Rightarrow \] \[{{a}_{1}}=2{{a}_{2}}\] \[\Rightarrow \] \[{{a}_{1}}=2{{a}_{2}}\] \[\Rightarrow \] \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{2}{1}\]
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