The 60 HZ AC power to an incandescent bulb can be measured with a phototransistor. To insure I wasn't picking up power line noise, I used battery power. Also simply shadowing the phototransistor cancelled out the signal so I was sure the EMI in the room wasn't causing the signal. I was surprised the thermal time constant of the bulb could be measured at 60Hz (filament is cooling enough to measure an intensity change in 1/120th of a second). Remember that a bulb gets power on positive and negative AC half-cycle.

There are circuits that inject small signals into AC power lines. Google "X-10 protocol". This is an old 1980s technology for controlling lamps through your house with small injected signals. Microchip has an app note but, because the app note doesn't not use transformers, and instead uses capacitive or resistive voltage drops from mains to semiconductor controllers, those links get killed on this site (transformerless is a forbidden topic here - but Google will work for you).

 

The mains supply has a non-constant amplitude and already carries a lot of noise. You will need good filtering to distinguish the effects of that from the effects of your added noise.

 

Just use a low voltage bulb and run it off the output of a audio amplifier of similar wattage rating to the bulb then feed the input of the amplifier with whatever frequency or set of frequencies you wish to test with and record your data from there.

I think that's probably the best approach if you can use a low voltage and power bulb (such as a 12V auto bulb) for your tests.
It means you will have a clean output and full control of the noise.
You will need to sum the output of a 60Hz generator with the noise generator into the audio amplifier.

 

A triac/optocoupler could be used to 'randomly' remove cyles/partial cycles of the incoming AC .

 

I'm rather wondering what effects are to be expected and to what degree of precision and accuracy the various observational measurements are to be done at as well..

Reason being the operating effects and efficiency of a simple filament type incandescent bulb are pretty well known and changing the frequency or adding a bunch of complex variation in the power supplied to a bulb doesn't really change much in terms of what degree of illumination Vs heat or other emissions it makes.

As far as I know a incandescent bulb follows a pretty well defined working principle and highly predictable process of operation well defined by the laws of physics.

 

Connect an inductor in series with the bulb with a value that has a high reactance to the applied signal but low reactance to 60Hz.

How much bigger would the reactance value have to be at the applied signal? Also I have done something similar to this in the past with two inductors one going to hot and one to neutral although I did not design the circuit so I don't know the reasoning. I would prefer to use the lower voltage idea as it is easier but I don't think I will be able to.

 

How much bigger would the reactance value have to be at the applied signal?

It depends upon how much the signal generator can drive.
Assuming 50 ohms, then you would want the reactance to be at least that high at the lowest test frequency.

 

I'm rather wondering what effects are to be expected and to what degree of precision and accuracy the various observational measurements are to be done at as well..

Reason being the operating effects and efficiency of a simple filament type incandescent bulb are pretty well known and changing the frequency or adding a bunch of complex variation in the power supplied to a bulb doesn't really change much in terms of what degree of illumination Vs heat or other emissions it makes.

As far as I know a incandescent bulb follows a pretty well defined working principle and highly predictable process of operation well defined by the laws of physics.

There's no way these experiments will have the precision to uncover anything that wasn't predictable in the first place based on solid physics that won't benefit from being rediscovered.