A) 25 : 1
B) 5 : 1
C) 9 : 4
D) 25 : 16
Correct Answer: C
Solution :
Let \[{{a}_{1}}\]and \[{{a}_{2}}\]be amplitudes of the two waves. For maximum intensity \[{{I}_{\max }}={{({{a}_{2}}+{{a}_{2}})}^{2}}\] For minimum intensity \[{{I}_{\min }}={{({{a}_{1}}-{{a}_{2}})}^{2}}\] Given, \[\frac{{{I}_{\max }}}{{{I}_{\min }}}=\frac{25}{1}=\frac{{{({{a}_{1}}+{{a}_{2}})}^{2}}}{{{({{a}_{1}}-{{a}_{2}})}^{2}}}\] \[\Rightarrow \] \[\frac{{{a}_{1}}+{{a}_{2}}}{{{a}_{1}}-{{a}_{2}}}=\frac{5}{1}\Rightarrow \frac{{{a}_{1}}}{{{a}_{2}}}=\frac{3}{2}\] (law of componendo and dividendo) Also, Intensity \[\propto \]\[{{(amplitude)}^{2}}\] \[\therefore \] \[\frac{{{I}_{1}}}{{{I}_{2}}}={{\left( \frac{{{a}_{1}}}{{{a}_{2}}} \right)}^{2}}=\frac{9}{4}\]
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