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. $450cm{s}^{-1}$
• D. $150cm{s}^{-1}$

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 $\frac{2\pi }{T}=60\pi$ $24\pi =60\pi$ $\Rightarrow$ $V=x\lambda =30\times 5=150cm{s}^{-1}$