Why your mic may be tricking you!
Even if you have started recording for just a little while, you've most likely heard about microphone polar patterns (and if you haven't, just go googling), that is to say the 3D shape showing how the microphone is picking up sound in the volume around its capsule.
There's a good chance that the first microphone you used was a cardioid one. You may even seen its polar pattern chart, that nice round graph showing how nicely your cardioid mic picks up frequencies mainly from the front, progressively attenuates the sound coming from the sides, and it's not supposed to pick up anything from the back.
That chart usually shows a 2D section of the volume around the capsule, "cut" on the same plane as the mic. An omni will have a spherical pickup volume, a cardioid will have a sphere with a "punched hole" in the back, a figure-8 will have two lobes front and back, and so forth.
So far, so good.
What you may or may not have discovered, however, is that polar pattern charts can be a little misleading for the inexperienced.
The main issue is that a microphone real pickup pattern generally changes with the frequency.
The nice graph you see in most manufacturers data sheet is taken measuring the mic response in an anechoic chamber (aka reflection-free room), often using a 1 KHz signal.
But the actual pickup pattern is often quite different at different frequencies. A mic can be cardioid at 1KHz but actually be a almost omni at 150Hz!
For example, as a rule of thumb, with a cardioid mic the lower the frequency, the more omnidirectional will the response become - meaning the rear rejection might be quite a bit less than you'd expect. And many omni mics don't really capture a "perfect circle" of sound energy at all frequency at all... but often have significant rear rejection for frequencies over 10 KHz. Which is why, incidentally, most omni still have some marking telling you where the "front" is.
There are (usually expensive) mics that are carefully engineered to have more or less consistent polar patterns across a very wide band of frequencies, but it's not really necessary.
For example, if you look at the response chart for the classic Shure SM58, you can see how it's cardioid at 500 Hz and 1000 Hz, but down at 125 Hz it picks up about 50% of the sound energy (i.e. moving air) reaching the back/sides, and a small "tail" of rear sensitivity appears at the dull singer fix - aka 8 KHz...
The first two measures give you an indication of why the 58 is a classic live vocal mic: it has great back rejection right in the vocal range. But that almost-omni response at 125 Hz tells you that you better engage that high-pass filter on the desk, to make it work together with loud kick and bass on stage.
Things are not that different with a 57 (often the mic of choice for guitar amplifiers): so it's better to engage that preamp hi-pass filter when tracking that Boogie in the corner! Especially when recording your guitar together with a full band, since kick and bass, if loud enough, will be picked up by the mic rear and filter the sound somewhat.
True, if you use a 57 to record the guitar amp alone, for an overdub, usually you will have moderate low frequency from the guitar... but not always: a guitar's low E goes down to about 82 Hz (and even lower if you like your guitar heavy and detuned) so bass trapping is still important to avoid reflections being picked up by the 57 and making a mushy mess of these heavy riffs you've been practicing so much.
Another interesting side effect is when recording strings (cello, viola, violin, you know) because their soundboard emit different frequencies in different directions. So a cardioid mic may end up filtering in certain way because it's more sensitive from back reflections at lower frequency; or even an omni mic might emphasize certain frequencies over certain others.
Whether this is good or not however, depends on the sound you're after.
That's because polar patterns which change with frequency are not necessarily a bad thing.
Those are properties that contribute to the "sound" of a specific microphone, either good or bad. The very fact that, for example, a mic rejects most of high frequency from the back, but lets a little low reflection pass, may well be the key to its "sound" - at least in a well-treated but-not-so-quite-anechoic room, like the ones in the real world. And it can be why the very same microphone produces bad recordings in a bad room.
It's one more reason for which it's impossible to judge mics by looking at technical data only - you have to deploy them in a reasonably sounding room and hear how they work! It's simply useful to be aware that the marketing names of microphone pick up characteristics may be.. well, marketing.
Just don't go around thinking that because a microphone is marketed as "cardioid", it will not pick up anything from the back!
All this said, the best manufactures publish polar pattern diagrams showing a handful of frequencies (using a different kind of dotted line), which makes much easier to account for these effects. These are for example Neumann, DPA, Shure. Sennheiser, but many more of course. I am always a little wary of manufacturers which don't, even if it's not necessarily a show stopper.
However, if a polar pattern is indeed different at different frequencies, you can get an idea on how it looks at a frequency not charted, by imagining a smooth 3D surface that connects vertically the various 2D shapes. As in the figure below (which is for varying omni sensitivity). So long the mic is not catastrophically bad, this "surface" should be imagined as generally smooth, but with small ripples or bumps - corresponding to frequencies where the mic is a little more sensitive (the "peaks" in the mic's frequency response chart).
It's also useful to note that not all microphones patterns are changing so much with frequency; nor they need to be "expensive" to be consistent in their pickup patterns.
Varying polar patterns are simply the result of the construction and design of a specific capsule.
The desirable sonic properties of a certain capsule design may outweigh the fact that, with that design, the polar pattern is frequency-dependent.
Simpler designs, less expensive to manufacture, can indeed lead to very stable polar patterns. For example, Røde's relatively inexpensive NT5s publish an almost perfectly circular pickup pattern at frequencies from 500 Hz to 4 KHz and indeed are extremely good mics, working very well as omnis in all situations.
Good manufacturers test (or should test) their mics in the field.
It's also not so that the "best sounding" mics are the ones whose polar pattern changes less with frequency. An U87ai in cardioid mode has also quite changing patterns at different frequencies (go have a look at Neumann's published charts for the 87), but nobody would dream to say that it's a bad mic.
And when pattern do change dramatically at low or high frequencies, it's not necessarily an issue - since high- and low-pass filters on preamps and desks are there exactly to band pass and control what gets recorded and what doesn't.
What matters is that, when it comes to pickup sensitivity, you are aware of how the mic you're using "sees" different frequencies (or not), so that you can set up your gear and EQ to get the sound you want.
What about testing polar patterns by yourself?
Well, it's hard to test a specific microphone behavior precisely without an anechoic chamber (and setting up one is far from easy or cheap).
But if you have a good sounding room you may get an idea of a mic behavior by recording a sweeping tone in the audible range (while keeping the volume down to minimize the energy of reflections), and orienting the sound source to hit the side of the microphone you want to check (typically the back for cardioid mics or the sides for figure-8 ones).
In a non-perfectly absorbing room, it's inevitable that reflections and filtering will happen. So that test result won't be something to publish. But it will still give you an idea on how your specific mic performs in your specific room, or in a similar real-world situation.
It may be worthwhile information - if somewhat unscientific and limited to the room and position you have tested. Besides, it's fun.