I have found the cause of the no-sound problem:
It's the way the iPhone detects accessories connected to the 30pin dock connector. It does this by measuring the electrical resistance from pin 21 to ground. See here: http://www.allpinouts.org/index.php/A...
And the critical threshold values seem to have been changed in ios7. That is why the problem appears after the update.
The ad-hoc solution:
1) Clean the dock connector, using a toothbrush and a just a few drops of some solvent (I used window cleaning agent).
2) repeat 1)
while repeating 1) keep pressing the Volume up-down buttons (alternating, not at the same time) and check wether you see just a gray icon with OR without the volume bars changing while pressing the buttons. If NO bars are visible it means that the iPhone thinks it's docked although it's not.