A) 3
B) \[\frac{3}{\pi }\]
C) \[\frac{6}{\pi }\]
D) 6
Correct Answer: B
Solution :
The given equations of waves be written as \[{{y}_{1}}=0.25\,\,\sin (310\,\,t)\] ... (i) and \[{{y}_{2}}=0.25\,\,\sin (316\,\,t)\] ? (ii) Comparing Eqs. (i) and (ii) with the standard wave equation, written as \[y=a\,\,\sin (\omega t)\] ... (iii) We have, \[{{\omega }_{1}}=310\] \[\Rightarrow \] \[{{f}_{1}}=\frac{310}{2\pi }\]unit and \[{{\omega }_{2}}=316\] \[\Rightarrow \] \[{{f}_{2}}=\frac{316}{2\pi }\]unit Hence, beat frequency \[={{f}_{2}}-{{f}_{1}}\] =\[\frac{316}{2\pi }-\frac{310}{2\pi }\] \[=\frac{3}{\pi }\]unit
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