A) \[c=\frac{1}{\pi a}\]
B) \[c=\pi a\]
C) \[b=ac\]
D) \[b=\frac{1}{ac}\]
E) \[a=bc\]
Correct Answer: A
Solution :
The maximum particle velocity is twice the wave velocity \[a\omega =2\left( \frac{\omega }{k} \right)\] or \[ak=2\] .... (i) Given \[y=a\sin 2\pi (bt-cx)\] or \[y=a\sin (2\pi bt-2\pi cx)\] The general wave equation \[y=a\sin (\omega t-kx)\] then \[k=2\pi c\] \[\therefore \] \[a2\pi c=2\] [From Eq. (i)] or \[c=\frac{1}{\pi a}\]
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