A) 400 m/s
B) 300 m/s
C) 200in/s
D) 100 m/s
Correct Answer: C
Solution :
Here: Equation of the standing wave is \[y=0.3\sin (314t-1.57x)\] ...(1) The standard equation of standing wave is \[y=a\sin 2\pi .\left[ \frac{t}{T}-\frac{x}{\lambda } \right]\] Comparing the given equation (1) and standard equation (2), we get \[y=0.3\sin \left[ \frac{314t}{2\pi }-\frac{1.57}{\lambda } \right]\] ...(2) \[=\frac{0.30}{100}\sin 2\pi \left( 50t-\frac{x}{4} \right)\] Or \[\frac{1}{T}=50\] and \[\lambda =4\] Hence, the velocity of the standing wave is \[\upsilon =n\lambda =\frac{1}{T}\times 4=50\times 4=200m/s\]
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