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(C) In a stationary wave,the points where the amplitude of vibration is zero are called nodes,and the points where the amplitude is maximum are called

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$4$

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(C) In a stationary wave,the points where the amplitude of vibration is zero are called nodes,and the points where the amplitude is maximum are called antinodes.Paper pieces placed at antinodes will fall off due to maximum vibration,while a paper piece placed at a node will remain on the wire because the amplitude of vibration at a node is zero.Since the middle piece of paper does not fall,it must be located at a node.The distance between the two supports $Q$ and $R$ is $L = 4x$.Given that the middle piece is at a node,the wire vibrates in two loops (each of length $2x$).The length of one loop is $\frac{\lambda}{2}$.Therefore,$2x = \frac{\lambda}{2}$,which gives $\lambda = 4x$.Thus,the wavelength of the vibration is $4x$.

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