Thanks to both you and RobertoS for your advice. I'll pass it on to our tech guys.
The phone insatllation is quite old, and only has an old-style master socket with no removable faceplate.
The existing setup is as follows:
One master socket, fitted with a two piggybacked doublers (Don't ask me why?)
The remaining socket on the first doubler has a filter and is connected to the BB computer.
Both sockets on the second doubler have filters.
Filter 1 feeds the answerphone, which has a payphone attached
Filter 2 feeds the desk where the studio phone is attached.
Filters fitted to both doubler outlets.
Seems to me there are too many doublers in use, and the setup should be either:
1 Doubler, with filters on both sockets
Filter 1 feeds an answerphone, which has a payphone attached.
Filter 1 is also used for the BB computer
Filter 2 feeds to the broadcast desk, the studio phone is connected to the desk.
or
Master socket with filter attached
Doubler in filter
Doubler socket 1 to Answerphone + Payphone
Doubler socket 2 to desk + studio phone
Filter to BB computer
The cable runs for the desk and the computer are about 25 - 30 feet
The studio phone is an ancient 'dial' type with a flashing neon in the handset, so it rings silent in the studio.
I hope this all makes sense.
Just had another thought, could it be a REN problem?
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