This behavior can also occur with the AppleVision 750 AV Display.
When the Macintosh audio is connected to these displays, you cannot hear the complete startup tone. Because of the additional features in the these displays, there is a slight delay in power reaching all the components. Depending on how quickly the speakers in the display are able to power up, you may hear a partial startup tone, no startup tone, or the entire startup tone.
There is nothing wrong with your display or your computer. If you want to hear the startup chime, unplug the sound out cable that connects from your computer to the display. Once this cable is removed, you hear the chime from the built-in speaker of your computer. Until you reconnect the sound cable, all sound goes through the internal computer speaker.