Final answer:
The device used to muffle the sound of a string instrument by being placed on the bridge is called a mute.
Step-by-step explanation:
The device placed on the bridge of string instruments to muffle the sound is called a mute. String instruments such as violins and guitars use resonance in their sounding boxes to amplify and enrich the sound created by their vibrating strings. The bridge and supports couple the string vibrations to the sounding boxes and air within. When a mute is applied, it dampens the vibrations, resulting in a softer and more subdued sound. This can be particularly useful in orchestral or chamber music settings where a composer or conductor desires a certain tonal or volume effect.