Q.

Standing waves are established on a string of length L such that A is a node and B is an immediate anti node. Oscillation amplitude for point B is a0 .Let a' be the oscillation amplitude for point C. Pick the suitable option(s) for correct value of a' and the possible equation(s) for standing waves on the string.

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a

a'=a02

b

y=a0sin6πLXcosωt

c

a'=a0

d

y=a0sin3πXLsinωt

answer is 3,4.

(Detailed Solution Below)

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Detailed Solution

y=a0sin⁡(kx)sin⁡(ωt+ϕ) kL3=nπ and kL2=n+12π ⇒n=1,k=3πL Also a′=a0sin⁡3πL×5L6=a0

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