Most shrill sounds are associated with belts, might be caused by different things: slippage due to exposure to liquids (coolant leaks, etc.), over or under-tension, etc. Cheapest option would be to change the accessory belt and see if it does make any difference.
In my opinion, water pump bearing failure is caused either by too old pump (and the rest of the components, e.g. the belts are likely to be as worn or break before that happen), or by incorrect belt tension so unlikely to be that. it could be the water pump that leaks and cause exposure of coolant on the belt so worth checking the water pump if possible. Alternator pulley is a "complex" part and not always sold separately from the alternator, but I'm not sure it is associated with failure usually so I would check the accessory belt first. What's the car/engine?
Most shrill sounds are associated with belts, might be caused by different things: slippage due to exposure to liquids (coolant leaks, etc.), over or under-tension, etc. Cheapest option would be to change the accessory belt and see if it does make any difference.
In my opinion, water pump bearing failure is caused either by too old pump (and the rest of the components, e.g. the belts are likely to be as worn or break before that happen), or by incorrect belt tension so unlikely to be that. it could be the water pump that leaks and cause exposure of coolant on the belt so worth checking the water pump if possible. Alternator pulley is a "complex" part and not always sold separately from the alternator, but I'm not sure it is associated with failure usually so I would check the accessory belt first. What's the car/engine?