A) 10-2 m/s
B) 10-4 m/s
C) 1 m/s
D) 104 m/s
Correct Answer: D
Solution :
Key Idea: The standard equation of standing wave is given by \[y=2a\sin \,\omega t\,\cos kx.\] Let y be the displacement, a the amplitude, \[\omega \] angular frequency, then standard equation of standing wave is \[y=2a\sin \,\omega t\,\cos kx\] ?(i) Given equation is \[y=a\,\sin (100\,t)cos\,(0.01x)\] ?(ii) comparing Eqs. (i) and (ii), we get \[\omega t=100\,t\] \[\Rightarrow \] \[\omega =100\,\,rad/s\] \[kx=0.01\,x\] \[\Rightarrow \] \[k=0.01\,{{\text{m}}^{-1}}\] Also relation between velocity (v) frequency \[(f)\], wavelength \[(\lambda )\] is \[v=f\lambda \] Putting \[\lambda =\frac{2\pi }{k},f=\frac{\omega }{2\pi },\]we have \[v=\frac{2\pi }{k}\times \frac{\omega }{2\pi }=\frac{\omega }{k}=\frac{100}{0.01}={{10}^{4}}\,m/s\]
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