Final answer:
Increasing the frequency of a wave on a string decreases its wavelength while the wave speed remains the same. To determine the wave speed, measurements of the distance between the two posts that the string is attached to are required.
Step-by-step explanation:
When the frequency of a vibrating string is increased, the wavelength of the sinusoidal traveling wave decreases. This is because the wavelength (λ) is inversely proportional to the frequency (f), following the wave equation v = fλ, where v is the wave speed. The wave speed itself doesn't change with frequency if the medium remains the same, because it is determined by the properties of that medium. Therefore, the correct answer is that only the wavelength changes.
For measuring the wave speed on a string, students need to measure the distance between the two posts the string is attached to. This is because the wave speed (v) can be calculated by dividing the wavelength (which is twice the distance between the posts for the first harmonic) by the period, or alternatively, by multiplying the wavelength by the frequency of the wave.
Amplitude is not a factor in determining the speed of the wave on a string; amplitude affects the energy carried by the wave, not its speed. On the other hand, the tension in the string does affect the speed of the wave, but it does not need to be directly measured if one can observe the wavelength and frequency of the standing waves created.