There is also a difference between people motivated internally and externally. Internal motivated people tend not to required external sources of positive reinforcement. These people function and perform well and if I was to guess whether they needed music to hit a PR I'd say no.
Externally motivated people need a lot of encouragement - this is not a problem - just that this needs to be recognised in a workplace setting and identified in how they train.
I'm with Stu on telling people. But tell people of value. Your spouse, best friend etc not Tom, Dick and Harry on the internet as X mentioned. Your integrity will ensure that you fulfill it. Some call it integrity others pride, but heck whatever gets the job done.
If you keep it a personal goal, not tell anyone and work towards it and achieved it, I'd expect your motivation to be very strong both in and out of the gym.
Of course people possess both traits and can deploy them in whichever manner suits them but one motivator (external or internal) will dominate.