What method are you using to connect your device to your big Jambox? Wired or wireless (Bluetooth)?
Before you go and try to replace the speaker part as mentioned in previous answer (which take a lot of effort & will void warranty), you should test whether it's a connection issue.
If you are connected via Bluetooth, try to re-pair you device with the speaker again. On occasion, Bluetooth connections between two devices can get disrupted (due to poor range, different Bluetooth protocols or something else) & therefore cause interference (especially with wireless speakers). For most Bluetooth issues, a simple process of unpairing & re-pairing your devices will resolve the problem.
If you are connected via wired (AUX cable to 3.5mm jack),the problem could be with the AUX cable itself. Try replacing the cable first (they should be relatively cheap & easy to source @ any local electrical or Hifi store) to see if this fixes the noise issue. If the issue is not the cable itself, then you can also try to clean the inputs on each device. Sometimes dirt, dust & other build-up can happen inside the AUX inputs themselves & therefore cause static & disruption to the audio quality.
However, if both of these alternatives does not resolve your issue, then it's best to contact Jawbone support for further help!
Hope this helps!