Doppler. Fading.
Slinky sounds consist of altered frequencies if the slinky is in relative motion to the wave; the wave velocity depends on tension and pitch, so there will be an acoustic/longitudinal wave interaction.
Note that just playing with a slinky, needn't involve these effects specifically: lots of noise sources are impulsive in nature (i.e., fumbling around with it, hitting parts on a surface, or some loops get overlapped then twang apart, etc.), and the medium itself is dispersive, that is, frequencies travel at different velocities. Partly because, due to how the helix is shaped, higher frequencies (waves with tighter curvature) see more stiffness, and therefore a higher velocity; partly because there are multiple wave modes (stretching, bending, twisting) in the material, which all move at different rates so an impulsive wave spreads out into ripples.
Which is also what ripples on a pond (gravity waves) do: they are dispersive so an impulse separates into ripples of varying amplitude. (Try it, take a close look at the ripples next time you see some propagating!)
Anyway, that's a possible example of Doppler effect, of a sort (the shaken slinky example). The more direct case is when the transmitter and receiver are in relative motion; or the wave medium itself is, which is also relevant here (not that you'll see many bodies of water where the flow is smooth enough to observe ripples in motion*). Which is a less familiar effect in the air, but should be a thing still.
*That said, you can also observe some of the more dramatic (nonlinear) wave effects when rapid flow is seen. Where flow is faster than wave velocity, it's supersonic and waves cannot propagate up the flow. Consider the step around the base of a water stream hitting a flat surface (sink, say): near the stream, the velocity is high, then as it spreads out radially, flow decelerates, and then kind of... *fwoomp* it poofs out to a turbulent pileup of slower flow. In this region, gravity waves can propagate; of course waves all pile up near the shock front, making it very turbulent, but away from there, normal behavior can be seen.
As for fading, this still tends to be very frequency dependent (due to interference effects), but generally it occurs with an array of reflectors moving slowly, their reflections sometimes overlapping a target area, sometimes avoiding it completely. The classic radio example is ionospheric fading in sky-wave SW propagation; ionospheric layers vary in conductivity, much as the aurora forms shimmering, undulating sheets -- the coincidence is no accident, of course! A similar effect occurs in a busy environment, at lower radio frequencies -- multipath. (If you listen to FM radio in the car much, you've probably noticed it sometimes fades out. Creep forward about a quarter wavelength -- 0.75m -- and it likely comes back.) Or weird acoustic effects over distance, like maybe you can hear fireworks or factory noises at certain distances (some miles) but not others, give or take weather conditions (layered air is refractive, and can also trap sound by atmospheric ducting).
To be clear, many of these effects are frequency dependent -- due to interference. So you might not see them with visible light for example, where the scale is just so tiny (100s nm), or at best you see rainbow fringing. (Bubbles and oil slicks are indeed interference effects; these structures are thin enough, and consistently so, that you can make out the fringes, rather than it being a gray blur of all colors smeared together.) And whereas it looks like fading for a given radio channel, say, adjacent channels fade at different times/locations (with respect to receiver/antenna location that is).
On a more abstract level, amplitude: easy, just vary how much power goes from transmitter to receiver somehow. Block line of sight, cause interference, add a filter, etc. Frequency: a lot harder, you can't do this with linear processes.
Tim
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