When transformer's sinewave voltage becomes smaller (at the peak) than capacitor's voltage diode becomes reverse polarized. In spite of reverse polarization it will conduct for a moment in reverse direction (limited response), to snap back to zero. Fast diodes like Schottkys respond faster but also snap back faster creating very short current spikes. Amplitude of the spike in not as important as time. Extremely short spikes or fast changes (dv/dt) can couple to any, even smallest inductance in the circuit. Soft diodes, like HEXFREDs snap back slower. Is it audible? I suspect it depends on the circuit. It will likely do more harm in DAC circuit (containing clock) than in power amp, but I've never compared different diodes.
Here is article about it with drawings that will help:
https://www.allaboutcircuits.com/technical-articles/fast-ultrafast-soft-standard-schottky-selecting-the-right-rectifier/
