Final answer:
The speed of a traveling wave is determined by the properties of the medium it travels through, including its elastic and inertial characteristics, not by the wave's amplitude or energy.
Step-by-step explanation:
The factor that affects the speed of a traveling wave is the properties of the medium through which the wave travels. This encompasses the elastic and inertial properties of the medium. The wave speed is not directly affected by the wave's amplitude, the height of its crest and trough, or by the energy contained within the wave, although the energy is proportional to the square of the amplitude.
The speed of sound, for instance, is determined by the temperature, humidity, and composition of the air it moves through, rather than by the frequency or amplitude of the sound wave itself. For a mechanical wave, such as one traveling through a guitar string, the wave speed is influenced by factors like the string's tension and its linear mass density. Ultimately, the wave's speed determines how quickly the wave travels through the medium.