This always happens to me when I play classic minecraft online,but when I redownload minecraft about 2 times the sound is becoming to come back,make sure your computer's sound is on,but I think it is Java and Minecraft that is the problem

Make sure you are connected to the internet and then logg on a server and the sounds download as you play.

Try what was stated above.

Did youtry turning your computers sound up?or headphones/speakers? :p

When this happens to me I reset minecraft and join again works every time for me.

Try reconnecting your internet...

I get the same problem every so often. Seems if your internet connection is maxing its download speed on something else (downloading games, uploading to youtube etc..) the sounds that you already have won't load up. If you cancel everything you are doing with your internet and load minecraft again sounds usually works.

For me this is a java problem. For some reason the version minecraft is on doesn't support it for some people. I have a great, high spec PC but nothing is working. I'm having to wait until the next update for my sounds to work again.

Try restarting the game, sometimes the sounds don't always work. Or:

_xeodite_Bro just log onto a server and the sounds will download

As he said: the sounds download automatically as you play, providing you have a working internet connection.
If you're still not able to get the sounds, I'm sure there will be somewhere from which you can obtain them.

This has been happening to me too. Try force updating.

Check that you haven't removed the sound from your PC completly. You usually have a sound off button on your keyboard, try toggling it.

When that happens to me I usually just restart Minecraft and it should start working.

Bro just log onto a server and the sounds will download