A) \[30000\,\,cm/s\]
B) \[200\,\,cm/s\]
C) \[150\,\,cm/s\]
D) \[2\,\,cm/s\]
Correct Answer: A
Solution :
Key Idea: compare the given equation with standard one. The standard equation of a plane progressive wave is \[y=a\,\sin \frac{2\,\pi }{\lambda }\left( v\,t-x \right)\] ?(1) Where \[\lambda \]is wavelength, \[v\] is velocity, \[t\] is time and a is amplitude. \[y=2\,\sin \,\pi \left( 200\,t-\frac{x}{150} \right)\] ?(2) Comparing Eqs. (1) and (2) \[\frac{2\pi }{\lambda }=\frac{\pi }{150}\] \[\Rightarrow \] \[\lambda =300\,\,cm\] And \[\frac{2\pi }{T}=200\pi \] \[\Rightarrow \] \[T=\frac{1}{100}s\] Frequency \[\left( n \right)\]=\[\frac{1}{T}=\frac{1}{1/100}=100\,Hz\]. Also velocity = frequency\[\times \]wavelength \[=100\times 300\] \[=30000\,cm/s.\]You need to login to perform this action.
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