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(A) At $t = 0$,the kinetic energy of the string is zero,which means all particles are at their extreme positions and their velocity is zero. As the st

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All particles between $A$ and $C$ are losing energy at this instant.

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(A) At $t = 0$,the kinetic energy of the string is zero,which means all particles are at their extreme positions and their velocity is zero. As the string moves towards the mean position,the particles gain kinetic energy. Particles between $A$ and $B$ have a displacement $y > 0$. As they move towards the mean position $(y = 0)$,their potential energy decreases and kinetic energy increases. Since the total energy is conserved,if kinetic energy increases,the potential energy must decrease. However,the question asks about 'losing energy'. In a standing wave,particles oscillate. At $t=0$,they are at maximum displacement. As they move toward the equilibrium position,they gain kinetic energy. Looking at the motion,particles between $A$ and $B$ are moving towards the equilibrium position. Thus,they are gaining kinetic energy. Actually,the question implies the rate of change of energy. Since all particles are at extreme positions,their velocity is zero. As they move towards the mean position,they gain kinetic energy. None of the particles are 'losing' energy at this instant as they are all at the extreme position and about to move towards the mean position. However,if we consider the standard interpretation of such problems,the particles between $A$ and $B$ are moving towards the mean position,so they gain kinetic energy. Given the options,there might be a misunderstanding of the term 'losing energy'. If we consider the potential energy,it is maximum at the extreme position. As they move to the mean position,potential energy is converted to kinetic energy. Thus,they are 'losing' potential energy. Therefore,all particles between $A$ and $B$ are losing potential energy. Since $C$ is between $A$ and $B$,particles between $A$ and $C$ are losing potential energy. Thus,option $A$ is the most appropriate description.

$A$ standing wave is established in a single loop. At $t = 0$,the kinetic energy $(K.E.)$ of the string is zero. Choose the correct option.

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