Question

The vibration of string can be described by the equation $ y=0.75\,\{\cos \,(2\pi /5)x\}\sin \{(60\,\pi {{s}^{-1}})t\} $ The speed of wave travelling in the string is

• A. $ 24\,\,\pi \,cm\,{{s}^{-1}} $
• B. $ 0.3\,\,\pi \,cm\,{{s}^{-1}} $
• C. $ 450\,\,cm\,{{s}^{-1}} $
• D. $ 150\,\,cm\,{{s}^{-1}} $

Answer 1

Answer: (D)

Given equation $ Y=(0.75)\left\{ \cos \frac{2\pi }{5}\times \sin \,(60\pi )t \right\} $ Comparing this with standard equation $ y=a\cos \frac{2\pi }{\lambda }x\,\sin \frac{2\pi }{T}\times t $ We get $ \frac{2\pi }{5}=\frac{2\pi }{\lambda }\Rightarrow \lambda =5 $ $ \because $ $ n=30 $ and $ \frac{2\pi }{T}=60\,\pi $ $ 24\,\pi =60\,\pi $ $ \Rightarrow $ $ V=x\lambda =30\times 5=150\,cm\,{{s}^{-1}} $