* Wave speed depends on the medium: The speed of a wave is determined by the properties of the medium it travels through. In this case, the rope. Specifically, it depends on the tension in the rope and its linear density (mass per unit length).
* Frequency and wavelength are related: Frequency (how many waves pass a point per second) and wavelength (the distance between two crests or troughs) are inversely proportional. If you double the frequency, you will halve the wavelength.
* The relationship: The wave speed (v) is related to frequency (f) and wavelength (λ) by the equation:
v = fλ
Since you're changing the frequency and wavelength in a way that keeps their product constant, the wave speed remains unchanged.
