There are many possible causes for this issue. Take each of the following steps that you haven't already tried. Some may not apply to your model. Back up all data before making any changes.
1. Start with the steps recommended in this support article. Don't skip any of the steps. It's the starting point for further efforts to solve the problem.
2. Make sure you have a fully up-to-date installation of OS X.
3. If you've installed an application called "Memory Clean" or any other third-party software that is supposed to "clean" or "purge" memory automatically, remove it according to the developer's instructions and restart. You should do that even if the software is not causing the problem, because it's useless.
4. Other third-party software that has been reported to interfere with sound output includes "Boom" and "Samsung Kies." If applicable, uninstall according to the developer's instructions (not by dragging something to the Trash.)
5. If an AirPlay device is selected for sound output from iTunes (or from other applications via third-party software such as "Airfoil"), deselect it.
6. Launch the application "Audio MIDI Setup" by entering the first few letters of its name in a Spotlight search and selecting it in the results (it should be at the top.) Select Built-in Output from the list on the left. If the Mute boxes are checked, uncheck them.
7. If a red light is visible in the audio-out port when sound should be playing, the internal switch is stuck in the position for digital output. You may be able to free it by inserting and removing a mini-stereo jack of the proper size. If not, the machine needs to be serviced. Inserting any kind of tool in the port may cause damage that won't be covered by the warranty.
If there's no red light, the switch may still be stuck in the headphone position. Try to free it the same way.
8. Disconnect all wired peripherals except keyboard and mouse, if applicable. If more than one display is connected, disconnect all extra ones. Restart and test.
9. If you have a MacBook Air, turn off Bluetooth and restart.
10. Start up in safe mode. Don't log in; just restart as usual when the login screen appears. When you do, make sure the words "Safe Boot" do not appear in the login screen. If they do, the system is still in safe mode and sound won't work.
11. Reset the NVRAM.
12. Reset the SMC.
13. Triple-click anywhere in the line below on this page to select it:
/Library/Preferences/Audio
Right-click or control-click the highlighted line and select
Services ▹ Reveal in Finder (or just Reveal)
from the contextual menu.* A folder should open with an item selected. Move the selected item to the Trash. You may be prompted for your administrator login password. Restart the computer and empty the Trash. Recreate your settings in the Sound preference pane.
*If you don't see the contextual menu item, copy the selected text to the Clipboard by pressing the key combination command-C. In the Finder, select
Go ▹ Go to Folder...
from the menu bar and paste into the box that opens by pressing command-V. You won't see what you pasted because a line break is included. Press return.
14. Reinstall OS X after backing up all data.
15. Make a "Genius" appointment at an Apple Store.
