A) 8 m
B) 10 m
C) 5 m
D) 32 m
Correct Answer: B
Solution :
The given equation of a progressive wave is \[y=3\sin \pi \left( \frac{t}{2}-\frac{x}{4} \right)=3\sin 2\pi \left( \frac{t}{4}-\frac{x}{8} \right)\] The standard equation of a progressive wave is \[y={{y}_{0}}\sin 2\pi \left( \frac{t}{T}-\frac{x}{\lambda } \right)\] Comparing these two equations, we get \[T=4s,\,\,\lambda =8m\] \[\therefore \]Velocity of wave, \[v=\frac{\lambda }{T}=\frac{8}{4}=2\,\,m{{s}^{-1}}\] Distance travelled by wave in time \[t\]is \[s=vt\] or \[s=2\times 5=10\,\,m\]
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