The LG E2351 does not have any built-in speakers so you will not get sound from it except by plugging headphones into it's headphone jack if using HDMI signal cable. I don't know if the headphone jack works when the monitor is connected via a DVI or VGA signal cable though.
The Lg e2351-BN monitor comes with a D-Sub and DVI connections so there is no way to get sound to the monitor. The Lg e2351VR-BN model does come with a HDMI port and a headphone jack.
Have you connected headphones to the monitor?