The umpire or line judge simply calls the ball out. They don't have to explain anything, but occassionally a player may ask the chair umpire to confirm the call. In major tournaments, there may be a challenge system in place that allows players to challenge a chair umpire's or line judge's call using replay cameras, but even then, the umpire doesn't have to explain anything, they just say whether the point will be replayed or they call a new score.
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A served tennis ball which touches the top of the net and then lands within the bounds of the appropriate service box is called a let. A let serve can be attempted again.
A served tennis ball which does not touch the net and lands within the bounds of the appropriate service box is a good serve. This ball has been successfully put into play.
A served tennis ball which touches the net and lands outside of the bounds of the appropriate service box is called a service fault. A fault means that one of two allowed service attempts per point has been unsuccessful.
A served tennis ball which clears the net and then lands outside of the bounds of the appropriate service box is called a service fault. Again, a fault means that one of two allowed service attempts per point has been unsuccessful.