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 be the amplitude, \[\omega \] angular velocity, k constant and \[x\] displacement, then equation of standing wave is \[y=a\sin (\omega t-kx)\] Given, equation is \[y=0.3\sin (314t-1.57x)\] On comparing the two equations, we have \[\omega t=314t\]and \[kx=1.57x\] \[\Rightarrow \] \[\omega =314\]and \[k=1.57\] \[\therefore \] velocity \[v=\frac{\omega }{k}=\frac{314}{1.57}=200\,\text{unit}\]
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