Mervyn. A normal fuel pump should have a quite, uninterrupted hum like a small electric motor. When failing it becomes noticably louder and erratic. The tone of noise coming from the fuel pump would go up and down and get louder, as though it was laboring to pump fuel. I could hear mine while driving the car. It shouldn't be that loud. You can listen to it by climbing under the car. Mine is located under the car, directly beneath the back seat. If it is louder than a humming electric motor, it's may be a good indication that it is going south on you.
You can replace the fuel pump without having to replace the fuel pump relay. If the fuel pump is bad, replace that first. If the car runs normally then your fuel pump relay is most likely OK.
'85 190e 2.3
'90 BMW 325i
"81 Mazda RX7