Pickleball is a very popular game but it is very noisy. The problem is that paddles are designed in a way that maximizes the noise created by the impact of a pickleball. A simple test of noise generation is to drop a pickleball on different surfaces, such as a table, the strings of a tennis racquet, or a paddle. The noise created by the strings of a racquet is barely audible. Other surfaces are much noisier. Surfaces with a large area act to amplify the noise because they vibrate and move more air. That is why pianos, guitars and violins have a soundboard. The strings by themselves vibrate and create a musical note, but without the soundboard, the sound created by the strings is difficult to hear. The strings are attached to the board, which vibrates at the same frequency as the strings, but the board moves a lot more air than the strings on their own, so the sound is much louder.
A paddle acts in a similar way to a soundboard. However, the sound is generated by the impact of the ball rather than any attached strings. The impact acts to bend the paddle which then vibrates back and forth in several different ways. The paddle bends in the middle and continues to vibrate for a short time after the ball bounces off the paddle. The vibrations are eventually dampened by the hand.
The duration of the impact and the amplitude of the vibration depend on both the stiffness of the ball and the stiffness of the paddle. The ball itself is relatively soft, but the paddle is very stiff. However, the ball is very light, with the result that the impact duration is very short, typically about 2 ms (i.e., 0.002 s). The duration is a good match to the vibration period of the paddle, which is about 1 ms. As a result, the paddle vibration amplitude is relatively large, so it makes a loud noise.
A solution to the noise problem would be to use a softer paddle or a paddle full of holes so it doesn't move as much air. That is why the impact of a pickleball with the strings of a racquet is barely audible. The string surface is full of holes, so the area of the strings is only a small fraction of the total area of the racquet head. In addition, the strings are softer than a paddle, so the impact duration is longer. As a result, the ball sits on the strings for several vibration cycles of the strings and acts to dampen the string vibrations.
The same effect occurs if a bell is struck by a tennis ball. The sound is faint since the ball is soft and dampens the vibrations. If a bell is struck with a steel ball, the sound will be much louder. The combination of a pickleball with a paddle is like a bell struck with a steel ball. The simplest way to reduce the noise is to use a softer ball or a softer paddle. The ball is already quite soft, so the simplest solution is to use a softer paddle that is full of holes. For example, the stiff honeycomb core could be replaced with a suitable foam that would also help to dampen the vibrations, or the paddle could be replaced by a small tennis racquet.