Why longer sound waves lead to lower frequencies and why shorter sound waves lead to higher frequencies?

Picture a pasta machine, squeezing spaghetti out of single hole at a

constant speed.

Every so often, the pasta master drops the knife that cuts the continuous

nerdle of pasta coming out of the machine.

The speed of the string coming out of the machine is constant.

The slower he chops, the longer the pieces are. The faster he chops, the

shorter the pieces are.

The product of

(how many times a minute he chops) multiplied by (the length of the pieces)

is always the same number ... it's the speed of the material coming out

through the hole.