I just had the same problem yesterday with my z. The sound on mine was more of a buzz and I noticed some the smell of gas vapors when I accelerated. Anyway here's what was wrong with mine. There is a filter that is a part of the emissions system, it recurculates the gas vapors. Mine was clogged and made this buzzing sound even when the engine was shut off (drove me nuts for about two hours). I you jack up the car the filter is in front of the left rear wheel under a cover. Two bolts hold the cover on and underneath is a round plastic filter with a hose clamped to each end. A mechanic blew through mine and unclogged it for the time being and said I would have to order a new filter ($25.00). Good luck
