Hi NTB
I noticed that the expected AC sine waves were not really uniform...
So, I have 2 questions,
1. could this indicate that the transformer could be faulty?
2. could the circuit following the point where the scope was attached be reducing the appearance of a sine wave?
A1. No- quite normal
A2. Yes- most definitely
What you are seeing is a perfectly normal waveform from a transformer secondary winding feeding a rectifier/reservoir capacitor, as the other members have explained. The waveform is actually a distorted sine wave. A diode will only pass current in one direction, that is when its anode is more positive than its cathode by about 0.8V. A reservoir capacitor is like a huge bucket that can store billions of electrons (in the case of an audio amplifier PSU, about 10
18 electrons). By the way, your scope measurements are absolutely fine too. There absolutely is no need for a 10:1 probe.
The flat tops on the sine wave are where the rectifying diodes start conducting and connect the transformer secondary to the reservoir capacitor, which is a very low impedance (resistance). At that time a large current flows into the reservoir capacitor to charge it up, as indicated by the small ramp on the extremities of the waveform. The large current, coupled with the output impedance (resistance) of the transformer secondary winding, causes a voltage drop, and hence the flat tops on the sine wave.
If you put your scope probe on the reservoir capacitor, you will see a saw-tooth voltage waveform (ripple voltage) where the reservoir capacitor is being charged and then discharged, a bit, when providing current to the amplifier, until the next peak of the sine wave comes along to charge the reservoir capacitor once again.
(if you don't mind, I would like to steal your image showing an actual equipment transformer secondary waveform, as it will be very useful for explaining PSUs in the future)
The attached image below shows what your amplifier power supply probably looks like.