My textbook states, 'The sound box has a large area, it sets a large volume of air into vibration, the frequency of which is same as that of the string. So due to resonance a loud sound is produced.'
My question is why isn't the air around the string (apart from the hollow body) resonating or resonating sufficiently enough to produce a loud sound without the need for a hollow body? Isn't the hollow body's volume of air negligible compared to 'room/area' where the string is played?
Best Answer
Yes, the room has a lot of air, but most of it isn't in direct contact with the vibrating string. In order for the string to make much sound, it needs to transfer some of its energy to the surrounding air, but there are a couple of issues which make that difficult.
Firstly, the string has a relatively small surface area, so it simply doesn't directly contact very much air.
Secondly, the string isn't very effective at transmitting its vibrations to the surrounding air. It's a bit like if you get a thin rod and wave it back and forth in water. Yes, it makes a few ripples, but the rod mostly just cuts through the water. But if you get a wide paddle and wave it around, then it's easy to make large waves in the water. Similarly, a vibrating string mostly just cuts through the air, rather than making useful pressure waves in it.
With air, it's even harder to effectively induce waves than in water, because it's so compressible. Obviously, pressure waves do travel through the air, but it's a lot harder to transmit such waves through a gas than through a denser, stiffer medium.
So stringed instruments generally have some kind of soundboard: a surface with a relatively large area that's in contact with a lot of air. The string can efficiently transmit its vibrations to the soundboard, and the soundboard can, in turn, transmit those vibrations to the air.
On a guitar, the soundboard is the front of the body. Here's a diagram, courtesy of Wikipedia:
The soundboard of a piano is inside the body:
(source)
An important concept here is acoustic impedance.
Unfortunately, that Wikipedia article is heavily technical and mathematical, without much physical detail.
The soundboard of a musical instrument, or the membrane of a loudspeaker, doesn't need to have a lot of back and forth movement. It just needs to vibrate relatively gently. Large movement wastes energy by causing bulk movement of the air, rather than inducing the desired pressure waves.