I have a Tektronix 531A tube oscilloscope from the late 50s. I recently bought some 20$ probes and noticed a lot of noise on the 0.005 volt/cm setting when that spring loaded hook attachment was clipped on. When I bring my hand in closer to the plastic of the probe the ripple on the scope goes crazy and when I'm actually holding the plastic, it goes off screen on the 0.005 volt/cm setting. When the spring loaded hook attachment is removed the noise level is normal and when I touch the scope's chassis with the same hand the probe is in, it returns to normal levels as well.
My question for this part would be if this was to be expected from a 20$ probe and if there is any way I can get less noise with this clip. One thing that I should've mentioned at the beginning was that my house is old and has no mains ground in any of the wall sockets. I mean the hole is there but it was never wired when the new standards came in. I have done my best to ground the machine from its ground clip in back to my radiator, which has solved a lot of noise problems already on the higher settings like 0.05 volts/cm. Now its just the noise at the 0.005 volts/cm as mentioned above.
This brings me to my second and last question. Is it safe to take measurements with a "floating" oscilloscope that has no mains reference/grounding? Will people be shocked if they're next to that radiator now? I have read that if your machine is grounded, it is safe to measure battery powered equipment, isolation transformer stuff and basically anything else that doesn't have a ground connection where the circuit can be completed.
But what if your scope is not grounded? (Haven't found much helpful information on this for such an old scope as mine although I have seen some for the newer scopes) Is it still safe to measure battery powered and isolated stuff or is that now dangerous?
P.S. I only do this for a hobby. I have basic understanding of electricity and use my tools to repair tube powered equipment where voltages are in the 500+- range. Is there any dangers I should be aware of and any fail safe techniques that I could use to save my oscilloscope because its the only one I've got.