When producing a wave, such as a transverse wave on a slinky, the speed of the wave is determined by the properties of the medium through which the wave propagates. In the case of a slinky, the speed of the wave depends on factors such as the tension in the slinky and the mass per unit length of the slinky.
When you manipulate the slinky to create the wave, you have control over the frequency of the wave, which is the number of complete oscillations (up and down movements) per unit of time. By moving the slinky up and down faster, you are increasing the frequency of the wave.
However, the speed of the wave itself is not directly changed by altering the frequency. The speed of the wave is a characteristic property of the medium, and it remains constant as long as the properties of the medium do not change. For example, if you were to change the tension in the slinky or alter its mass per unit length, the speed of the wave would be affected.
In summary, while you can change the frequency of the wave by manipulating the slinky faster or slower, the speed of the wave itself is determined by the properties of the medium and remains constant unless those properties change.