A) 4 beats per second with intensity ratio 25 : 16 between waxing and waning
B) 8 beats per second with intensity ratio 25 : 16 between waxing and waning
C) 8 beats per second with intensity ratio 81:1 between waxing and waning
D) 4 beats per second with intensity ratio 81:1 between waxing and waning
Correct Answer: D
Solution :
Given, \[{{y}_{1}}=4\sin 600\pi t\]and \[{{y}_{2}}=5\sin 60\pi t\]Comparing with general equation\[y=a\sin 2\pi ft\] we get,\[{{f}_{2}}=300Hz\] and \[{{f}_{2}}=304Hz\]Number of beats \[={{f}_{2}}-{{f}_{1}}=4\,{{s}^{-1}}\] \[\frac{{{\operatorname{I}}_{max}}}{{{\operatorname{I}}_{\text{min}}}}={{\left( \frac{{{a}_{1}}+{{a}_{2}}}{{{a}_{1}}-{{a}_{2}}} \right)}^{2}}\] \[={{\left( \frac{4+5}{4-5} \right)}^{2}}=\frac{81}{1}\]
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