Electronic – Why does a radio still work inside a metal box

The cable connector body must contact the chassis connector body, which is generally metal, conductive, and bolted to a conductive metal case. Therefore the only choice for the connector body is a connection to the equipment case.

This (the equipment case) is obviously grounded - to safety earth. There is no choice about this.

However it is common for safety earth connections to form ground loops or be connected to a noisy earth point shared with, e.g. multi-kilowatt triac dimmed lighting systems (i.e. spiky 50Hz waveforms.)

So audio equipment design must separate the two functions of an earth connection: safety, and noise reduction.

Connect external metalwork to a safety ground, without worrying about the noise on it.

Connect signal ground to a separate low noise ground, without worrying about whether it is fault-current rated.

And this dictates the need for a separate pin for signal ground connections.

When I worked in broadcast audio, "pin 1 is ground" was one of those rules we didn't even have to think about.

Consider many pieces of equipment connected to an audio mixer by XLR cable : there may be many signal ground connections - yet we must eliminate ground loops. There are options on some of these boxes to "float" the signal ground - isolate it from safety ground - using the signal cable to provide a signal ground reference from the mixer.

Shielding generally works like this: If you apply an electric field from outside, electrons of the box material will start to move along the field direction. So, the one side becomes negative, the other positive charged. The field of this charges will cancel out the outer field totally inside the box, so there you will not measure any field.

Same applies for EM waves from inside / outside, the electrons in the box just have to move forth and back all the time.

However, it's not possible to shield an electrostatic charge inside the box, therefore, you need to ground it. (And magnetostatic fields can only be shielded by a ferromagnetic box.)

So, in general, a metal box will shield all EM waves and external electrostatic fields to some degree.

But if the mobility of the electrons is insufficient for the frequency of the radiation, they may not be able to follow the field fast enough, and then, EM waves may penetrate the box in either direction. Insufficient means: Too high resistance of the box / too high frequency / too high amplitude. So, to improve the shielding, use a thicker box, another nested box, or better box material.

Shielded enclosures typically also have a resonance frequency at which the shielding is poor (depending on how well the contents absorb emissions at the resonant frequency), and some small intentional or accidental apertures that can allow emissions to enter and leave. The shielding effectiveness of an enclosure is a function of many things.