Water pump or crankshaft pulley?

[Marleez]

I hear this noise when I start the engine (cold start) the noise gets quiet as it's running. The colder the start. The louder the noise

[Linas.P]

It is very hard to say without hearing it. 

What is the mileage of the car? When was the last service done? 

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Ok I see there is other thread with video. Indeed sounds like bearing, but to say which one exactly is difficult. This may help you to identify which is the most likely offender based on where the sounds is coming from:

 

[Marleez]

Millage is 138k I had it serviced when I bought it. It wasnt making the noise at the time. 

[Linas.P]

If I would guess I look into Idler or Tensioner Pulleys first:

Both have large bearings which would be in line with the sound. Water pump is a scheduled maintenance item, not sure if it was 60/80 or 100k. If you have any history on the car then it would be worth checking if that was done on time, but I would say less likely. It would start leaking well before making such noise. Further, if I am not mistaken it doesn't even have bearing, but is rather lubricated by the coolant (I might be wrong thought). 

Last item on the list is alternator, but that would be quite unusual.

[Marleez]

Thank you. The garage will have a look. I'll send them these diagrams. Thanks

[Texas]

You sure it’s not the well known tapping that comes from the hydraulic valve lifters for a few seconds after the car had not been used for a while and the oil drains down out of the upper head area, it goes as soon as oil pressure is achieved. I have had it happen a few times and to be fair it does sound dreadful, if it was to happen every start then I would be worried, but only happens ( sometimes) when engine has not been used for a while ie weeks!

UPDATE: I have just watched the vid on the duplicate post about this!! And It is Not the Hydraulic Lifter problem!

[Linas.P]

32 minutes ago, Texas said:

You sure it’s not the well known tapping that comes from the hydraulic valve lifters for a few seconds after the car had not been used for a while and the oil drains down out of the upper head area, it goes as soon as oil pressure is achieved. I have had it happen a few times and to be fair it does sound dreadful, if it was to happen every start then I would be worried, but only happens ( sometimes) when engine has not been used for a while ie weeks!

UPDATE: I have just watched the vid on the duplicate post about this!! And It is Not the Hydraulic Lifter problem!

Yeah... almost made same comment before watching it.

The description kind of suites the lifters issues as they usually are loud to start with and then becomes quiet once oil starts flowing well. Hence my question about mileage and last service. But no this case sounds like balls in the bearing just running loose round the races.