Question

Why are stringed instruments like guitar provided with a hollow box?

Answer 1

Hint The natural frequencies of boxes are similar to the frequency of the strings of the instruments. Higher amplitudes of vibration correspond with a higher loudness of the sound.

Complete step by step answer
String instruments are considered as resonators, that is to say they allow oscillations to occur at higher amplitudes at some frequency called the resonant frequency than at other frequencies. This process is called resonance.
In general, resonance can be defined as a phenomenon in which the amplitude of a particular system increases due to the application of a periodic force whose frequency is equal to or similar to the natural frequency of the system. Resonance can occur in both mechanical systems and electromagnetic systems.
In string instruments, the boxes are designed such that they possess a natural frequency whose value is equal to or close to the frequency of the strings attached to it.
Hence, when these strings are vibrated, the boxes having a natural frequency close to the frequency of the string, is forced into vibration (a phenomenon termed force vibration) and creates resonance, which allows the amplitude of the vibration to increase, the large volume air in the box also is resonated by the boxes, hence allowing a louder sound to be heard.
Thus, we can conclude that stringed instruments are provided with hollow tubes to create resonance in the air within it to generate a louder sound.

Note
Forced vibration is not identical to resonance. Forced vibration is the phenomenon where a system is simply forced into vibrations due to a force or contact with another vibrating system. Resonance is when the new system is particularly forced to vibrate at its natural frequency thus allowing amplification of amplitudes. In other words, not all forced vibrating systems are in resonance, but all resonant systems are a result of forced vibration.