Wave motionHardBloom L3
Question
The equation of a standing wave in a string is given by y = A sin ωt sin kx. Distance between two points having amplitude A/2 may be:
Options
A.$\frac{5\pi}{6k}$
B.$\frac{2\pi}{3k}$
C.$\frac{7\pi}{6k}$
D.$\frac{5\pi}{3k}$
Solution
Sol. 
A sin kx = $\frac{Α}{2}$
⇒kx = $\frac{\pi}{6}$
⇒ x = $\frac{\pi}{6k}$
Alsoλ = $\frac{2\pi}{k}$
= $\frac{\pi}{k} - \frac{\pi}{3k}$ and $\frac{2\pi}{k} - \frac{\pi}{3k}$
= $\frac{2\pi}{3k}$ and $\frac{5\pi}{3k}$
Hence (B) & (D)
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