Does "the way I step and release on the gas pedal " mean the noise is present when the car is stationary and idling, and progressively gets louder, or more frentic/faster at the same rate that you are raising or lowering engine speed using the gas pedal? This may be due to a noise in the engine itself or in one of its fan belt driven ancilliaries. (alternator,water pump or air conditioning compressor) . Or maybe something is loose and constantly rattling/vibrating in harmony with the differing engine speeds.
Or do you mean the noise increases depending on how the car is being driven - eg noise is only present, or increases when the engine is having to work hard accelerating or hill climbing, but quieter if the car is cruising comfortably. If so it may be due to something thats loose but only vibrates at certain resonances .
The difference between the two is subtle but might help diagnose /locate the cause.
If it occurs when car is idling try listening with the aircon switched off, then listen for any change when aircon is switched on. . Also do the same with headlights on and then switched off and vice versa. This can put a different load on the alternator or compressor which might affect any noise its making. But in some cars doing either of these things can cause a slight drop in idle speed so try to allow for this when judging. . On some cars it drops momentarily then the ECU automatically makes adjustments, while on others there is no noticeable change. Even if you do notice a difference there may be no problem so dont get expensive repairs without first getting trusted expert opinion/diagnosis.
With the engine idling try holding onto things like the air cleaner box and pipe work to see if this momentarily stops noise. Be very careful of moving parts, or getting loose clothing, long hair caught up.. Mechanics sometime use stethoscopes to pin point a source of noise such rough bearings in a running alternator, water pump etc. But this takes experience to know how much noise is normal . Even good components can sound like a box of spanners through a mechanics stethoscope.
You could also try pin pointing noise using the sound recorder on a mobile phone etc, or maybe even down load a decibel measuring app onto the phone. . Again be careful of moving parts. If you can get a clear sound recording maybe download it to this site, although diagnosing noises remotely is very difficult.
BTW check your oil level is correct and the oil in good condition and check your coolant level is correct. (Poorly water pumps can leak)
