You can turn off sound for incoming calls by caller with the Samsung Galaxy S III by creating a silent audio file and configuring a contact's custom ring tone. The S III doesn't include a silent ring tone, but Samsung has included a default audio recording app called "Voice Recorder" that can be used to create the silent audio file.

Creating a Silent Audio File

You can create a silent audio file by opening the "Voice Recorder" app listed under the "Applications." Move to a place with as little ambient sound as possible during the recording process. Start the recording by tapping the "Record" icon and stop the recording by tapping the "Stop" icon. You need to record only about one second of empty audio. Voice Recorder will list all recorded audio files after you've finished recording; hold your finger on the silent recording to bring up the menu, select "Rename" and change the file name to "Silence."

Importing the Silent Ringtone

Open the "Contacts" app and select the caller you want to silence. Tap the arrow icon under the "Ringtone" heading to bring up the "Ringtones" menu and select the "Add" option. Choose the "Sound Picker" option, select the "Silence" file from the "Songs" tab and tap "Done" to import the Ringtone and disable the contact's call sound. You do not need to import the silent audio file again and can change other contacts to the silent ring tone by selecting it from the "Ringtones" menu.