Harmonic noise introduced when using an iPhone dock extension cable connected to a mic peripheral
What you are picking up is EMI from USB frame sync (most probably through the ground wire):


  Every millisecond (12000 full-bandwidth bit times), the USB host transmits a special SOF (start of frame) token, containing an 11-bit incrementing frame number in place of a device address. This is used to synchronize isochronous data flows. High-bandwidth USB 2.0 devices receive 7 additional duplicate SOF tokens per frame, each introducing a 125 µs "microframe" (60000 high-bandwidth bit times each).
  
  USB 2.0 added a PING token, which asks a device if it is ready to receive an OUT/DATA packet pair. The device responds with ACK, NAK, or STALL, as appropriate. This avoids the need to send the DATA packet if the device knows that it will just respond with NAK.


This could be avoided with a properly shielded extension cable. Note that even dockXtender only shields some of the wires:


  A revolutionary 2-tier shielding system puts all video and audio signals inside a separate shielding to reduce interference from the other signals traveling through the wire.


If you're the DIY type of person it should be quite easy to make your own extension cable using high quality shielded wires. You will probably only need to connect just a few of the 30 pins: USB (power, gnd, data+/-), all GNDs and maybe accessory/serial (enable, rx/tx). Make sure you also shield the soldering on the connector.