This happens to mine, and they are most definitely stainless, not aluminum. Our stainless sink gets the same way. I assume it's from all the minerals in our water. I have found that mixing up some Oxyclean and water and a couple of minutes' soak and a scrub with a plastic scrubber will get rid of it (both from the pan and from the sink). It comes right back, though.
I haven't found that it has any negative impact on the usability of the pans, and doesn't shorten the life significantly if the 14+ year old chef's pan I use almost daily is any indication.
I did a little more research, and it's definitely mineral haze. Recommended treatments are Barkeeper's Friend (mild oxalic acid) soak/scrub, or boiling some vinegar, either one followed by a thorough rinse. In theory, if the haze is left alone it could develop into buildup, which would begin to degrade performance, but in practice it's not an urgent worry.
So if it bugs you, clean it off with mild acid or oxygen bleach. But expect it to come right back. If you only removed it once a year, you'd be a couple of years ahead of my cleaning schedule, and I haven't seen any harm from it.
As you probably know, induction burners produce an alternating magnetic field that induces a current in the cookware. This process can produce attractive and repulsive forces as well that cause vibrations.
The problem can be caused not only by poor sandwiched construction but by an uneven bottom surface, or loose parts or lids.
I have read that some people have successfully used silicon baking pads to dampen the sound.
This page has some useful information on the subject:
http://theinductionsite.com/proandcon.shtml
Best Answer
One possible reason for this would be if the cooktop used induction, where rather than heating up, it used electromagnest to cause the pan to heat up. For this to work, the pan must be ferrous and able to be magnetized. Although stainless steel is made from iron, it isn't strongly magnetic, and thus will not work well on an induction cooker.
To test if this is the case, you can try pans from other materials and see if they have similar problems. Aluminium, copper, or ceramic cookware simply won't heat up at all. You can also try turning an element on high without a pan, and waiting a minute or two. If you can hold your hand above the element without feeling any heat, it's either an induction cooktop or defective.
If you place a cast iron or carbon steel pan on the element, wait another minute or two, and test again but can feel heat, then it's induction.
As you mentioned it's a new cooktop, if it's new because you bought it (and not because you've moved), find the manual, and if it's an induction cooker, it should proudly proclaim that fact, and list what types of pans are recommended.
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The next possibility is that if you're coming from a gas cooktop you may not be used to the speed of electric cookers. With a glass-topped cooker, it's difficult to see the size of the elements, and so you may only have one or two elements on the cooktop that are rated for fast boiling or other high-heat applications. You can try each of the burners in turn, and see if some of them heat up faster than others.
... but there's also a chance that the element is defective. I'd suggest calling their customer service number, or e-mailing them to ask about the cooktop.