The speed of a wave in a rope is affected by the properties of the rope - mainly, how tight it is pulled (tension) and its mass per length (linear density). Changes in either of these properties changes the wave speed. For a fixed frequency, a change in the wave speed will also change the wavelength of the wave.
Waves - Case Studies - Questions 12 Help
There are three similar versions of this question. Here is one of the versions:
Version 1:
The diagram at the right is a snapshot in time of a wave moving along a rope. Which diagram below represents a wave with the same frequency but moving through a different rope having one-fourth the linear density and pulled to the same tension? Tap on an image to select or deselect it.



Try these links to The Physics Classroom Tutorial for more help with understanding wave properties:
The Anatomy of a Wave (wavelength and amplitude)
The Speed of a Wave
The Wave Equation