When a violin string is tightened, the tension in the string increases. This causes the string to vibrate at a higher frequency, which produces a higher pitch. The higher the pitch, the louder the sound.
In addition, tightening a violin string also increases the amplitude of the vibrations. This means that the string moves more when it vibrates, which produces a louder sound.
Therefore, tightening a violin string will make it louder, not quieter.