Final answer:
Increasing the tension on a guitar's strings increases the wave speed and hence the frequency of the sound produced because the frequency of a wave is directly related to its speed. So, the wavelength does not decrease as a result. Option a) The wavelength of the wave decreases, is the correct answer.
Step-by-step explanation:
When the tension on a guitar's strings is increased, this increases the speed of waves on the string, resulting in a higher frequency of the sound produced. This occurs because the speed (v) of a wave is given by the formula v = √(T/μ), where T is the tension and μ (mu) is the linear density of the string. As the speed of the wave increases due to the increased tension but the length of the string remains the same, the frequency (f), which is related to speed and wavelength by the equation v = fλ (λ being the wavelength), must increase.
Since the speed of a wave is the product of its frequency and wavelength, and we know that the speed increased and the frequency must thereby increase, it follows that the wavelength does not decrease; otherwise, we could not account for the increased speed with an increasing frequency. Therefore, the correct answer from the options provided is a) The wavelength of the wave decreases. The mistakes in the other options include: b) The frequency of the wave decreases, which is incorrect because the frequency in fact increases. c) The amplitude of the wave increases doesn't necessarily relate to the tension of the string. d) The speed of the wave remains unchanged is incorrect, as the question specifies that the tension increase leads to increased wave speed.