A) 400 unit
B) 250 unit
C) 200 unit
D) 150 unit
Correct Answer: C
Solution :
Key Idea : Standard equation of standing wave is \[y=a\sin \,(\omega \,t-kx)\]. When two identical transverse, progressive waves travel in a bounded medium with the same speed but in opposite directions then by their superposition a new type of wave is produced which appears stationary in the medium. This is .called standing wave. Let a b the amplitude, o angular velocity, k constant and x displacement, then equation of standing wave is \[y=a\sin \,\,(\omega \,t-kx)\] Given, equation is \[y=0.3\sin \,\,(314\,t-1.57\,x)\] On comparing the two equations, we have \[\omega \,t=314\,t\] and \[k\,x=1.57\,x\] \[\Rightarrow \] \[\omega =314\] and \[k=1.57\] \[\therefore \] velocity \[v=\frac{\omega }{k}=\frac{314}{1.57}=200\] unit
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