I'm guessing the speakers are trying to take an audio signal from the cable, but either can not play it back (Dolby Digital/DTS, etc.), or there is no audio over the HDMI cable, so you just get static.
I had an Hannspree monitor with built-in speakers, an Nvidia graphics card and a ASUS motherboard with an integrated sound card. It turns out that to use the DVI 'out' there is a small S/PDIF cable that needs to be connected from the video card to the sound card (I guess to move the audio off the DVI port onto the sound card for output to the green audio 'out' port). Note that there is nothing in the Nvidia manual about connecting this cable.
However, the ASUS mother board that I have, for some reason does not support digital audio and thus does not have the S/PDIF connection node needed to connect to the cable from the graphic card. So when I connected the DVI -> HDMI cable to my monitor that has the internal speakers, there was no sound being transferred, which resulted in a loud crackling static as the speakers in the monitor looked for audio. Connecting a speaker wire from the sound card 'out' to the green audio 'in' on the monitor or 'muting' the audio did not eliminate or reduce the static.
To fix the issue, I had to buy a new graphics card (ATI HD 4550) that had an HMDI 'out' connection which I ran to the monitor's HDMI 'in'. Everything is working fine now.
This was probably not the most cost-effective solution to fix the problem - but it is fixed
Note: It was surprizing to me to find that most of the mid-price range graphics cards from Nvidia and ATI will have one or two DVI 'out' -- but no HDMI. It is also difficult to tell from the box exactly what output connections the cards have. Many said HDMI out - but it was through a DVI->HDMI adapter - which wouldn't have worked in my case. So I was somewhat limited in my choice of graphic cards that were available at my local Best Buy. Boy do I wish there was a Fry's or Micro Center in my area. Depending on Best Buy for computer hardware sucks! In this case I had to get it fixed immediately, so I didn't have time to wait for an on-line order to be shipped.