Wave motionHardBloom L1

Question

String of length L whose one end is x =0 vibrates according to the relations given by different equations. Choose the CORRECT statements.

Options

A.y = A sin$\frac{\pi x}{L}$sin ωt has 1 antinode, 2 nodes
B.y = A cos $\frac{\pi x}{L}$sin ωt has 2 antinodes, 1 node
C.y = A sin$\frac{2\pi x}{L}$sin ωt has 3 nodes, 2 antinodes
D.y = A cos $\frac{2\pi x}{L}$sin ωt has 3 antinodes, 2 nodes

Solution

Sol. (A) K = $\frac{\pi}{L}$ = $\frac{2\pi}{\lambda}$

⇒ L = $\frac{\lambda}{2}$

at x = 0, y = 0 ⇒ fixed end

(B) at x = 0, y = A ⇒ Free end

K = $\frac{\pi}{L}$⇒ L = $\frac{\lambda}{2}$

(C)& (D) check similar to (A) & (B)

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