Short Answer:
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The sound is caused by airflow across holes on the underside of the wings of certain aircraft.

Long Answer:
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I too have noted the sound phenomenon that you describe. [This video][1] has a great example between 0:26-52 (link starts playback at 0:26 where the noise starts):  
http://youtu.be/8g0TWFUDDtE?t=26

I will readily admit that this answer is mostly just a compilation of what I have learned researching this. Your question intrigued me and I've enjoyed learning about it!

As I discovered as I started researching this, many others are familiar with the noise as well. [This article on Airliners.net][2] had a lot of discussion about it, starting with a lot of interesting—but ultimately flawed—theories.

But, that thread led me to the answer to your question, which is: the sound is caused by the "circular opening used to equalise the pressure in wing fuel tanks", according to [Euractiv.com][3]

[This article on AirportWatch][4] further explains: 

> The Airbus 320 series of aircraft, [...] have been known for many years
> [...] to have a particularly irritating high pitched
> whine. This is caused by air rushing across the under-surface of the
> wing, where there are Fuel Over Pressure Protector (FOPP) cavities.
> This generates noise, in the same way as blowing air over the mouth of
> a bottle. Every A320 series aircraft emits a signature howling noise
> while approaching to land. It is heard most when the plane is
> travelling at around 160 knots, and the frequency is around 500-600Hz,
> which is close to peak sensitivity of the  human ear.

That being said, there is apparently a fix to that problem, as both the aforementioned links describe. As [Euractiv.com][3] explains, the fix is a vortex generator:

> a 5-cm triangular piece of aluminium sheet metal upstream of the two
> vents on each wing, in order to divert the air flow and stop the
> whistle. A decade of research went into the vortex generator, which
> stems from efforts to mask a similar whistle produced when air blows
> over the gun ports of warplanes.

This image shows both the FOPP hole, and the VG that softens the sound:

[![A320 FOPP and VG*Image Courtesy of Lufthansa*][5]][5][Image Courtesy of Lufthansa]

 Read the articles linked, interesting stuff therein!


  [1]: https://youtu.be/8g0TWFUDDtE?t=26
  [2]: http://www.airliners.net/aviation-forums/tech_ops/read.main/321412/
  [3]: http://www.euractiv.com/sections/aviation/small-beautiful-how-tiny-device-cuts-aircraft-noise-303505
  [4]: http://http://www.airportwatch.org.uk/2014/11/lufthansa-retrofitting-a320-family-with-simple-inexpensive-noise-reducing-device-to-stop-the-airbus-whine/
  [5]: https://i.sstatic.net/Gu0fM.jpg