The amount of sound produced by a drum is determined by a number of factors, including the size and thickness of the drumhead, the tension of the drumhead, and the force with which the drumhead is struck. When the drumhead is struck harder, it vibrates more vigorously and produces a stronger sound wave.
The relationship between the force of the strike and the loudness of the sound is not linear. In other words, doubling the force of the strike does not double the loudness of the sound. Instead, the loudness of the sound increases logarithmically, meaning that each doubling of the force of the strike produces a progressively smaller increase in loudness.
The logarithmic relationship between the force of the strike and the loudness of the sound is due to the way the human ear perceives sound. The ear is more sensitive to changes in loudness at lower levels than at higher levels. This is why a whisper can be heard in a quiet room, while a loud noise can be heard even from a distance.
The logarithmic relationship between the force of the strike and the loudness of the sound also explains why it is possible to play a drum very softly without producing a noticeable sound. This is because the ear is less sensitive to changes in loudness at lower levels.