Question

Why is the loudness of the sound heard by a plucked wire increased when it is mounted on a sound board?

Answer 1

Because the board provides comparatively a large area and forces a large volume of air to vibrate and thereby increases the sound energy reaching our ears.

Answer 2

When the strings are made to vibrate by plucking, the vibrations get transferred to the hollow sound box. As a result, the large volume of air in the box is also set into vibration to produce a loud sound. The larger the surface area of the air in the sound box, the louder the sound produced.