A) \[\lambda =2\,\pi A\]
B) \[\lambda =\pi A\]
C) \[\lambda =\pi A/2\]
D) \[\lambda =\pi A/4\]
Correct Answer: C
Solution :
The equation of given wave travelling with amplitude A is given by \[y=A\sin 2\pi \left( ft-\frac{x}{\lambda } \right)\] Maximum velocity\[{{v}_{m}}=A\omega =A\times 2\pi f\] Also, \[c=f\lambda \] \[\therefore \] \[{{v}_{m}}=\frac{A2\pi c}{\lambda }\] Given, \[{{v}_{m}}=4c,\]then \[4c=\frac{A.2\pi c}{\lambda }\] \[\Rightarrow \] \[\lambda =\frac{\pi A}{2}\]
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