When hum is not caused by a filter cap.

Audio tubes with heater to cathode leakage and defective cathode bypass components can also cause hum.  

If you don't know the words to the song when you hear hum, find a Sing Along With Mitch record.  They have the words on sheets you can pass around to your mates.....

FrankB wrote:

Of course some radios hum because they don't know the words to the song. 

I totally understand this! I have heard these hums numerous times, and I can't tell one song's hum from another. 

Of course some radios hum because they don't know the words to the song. 

Hum in transistor radios can be caused by the A.C. power supply defects with an linear (wall wart type) or internal type.
Most of the switching supplies create R.F. noise NOT A.C. HUM.


Hum in tube radios has a few causes .  
1 A failing or bad electrolytic capacitor.
2 A tunable hum is often caused by cathode-to-heater or it could be caused as a cathode to grid if it's a directly heated cathode filament short circuit.
3 Capacitors used to filter R.F. on the incoming hot side of A.C. power.

So the radio worked great then developed an intermittent hum and volume control didn't shut totally down.

Look for bad ground on low end of volume control wiper.
 I have seen this a few times over the years, especially on solid state equipment.