Final answer:
If the tension on the string is doubled, the velocity of the wave will change, which in turn affects the wavelength if the frequency is constant. To determine the original wave speed, students need to measure the distance between the two posts besides the oscillation time.
Step-by-step explanation:
If the tension on a string vibrating between two posts is doubled, the velocity of the wave will change. According to the formula for the wave speed v = √(T/μ), where T is the tension in the string and μ is the linear mass density, it's clear that the wave speed is directly proportional to the square root of the tension. Therefore, if the tension is doubled, the velocity will increase, but not double. The velocity will increase by a factor of the square root of 2 (approximately 1.414). This change in velocity impacts the wavelength, if the frequency is held constant, according to the wave equation v = f λ, where f is the frequency and λ is the wavelength.
To determine the speed of the wave on the string, students must measure the distance between the two posts in addition to the time it takes for the wave to oscillate. The amplitude of the wave and the tension in the string are not directly necessary for determining the wave speed unless the question pertains to changes in these values affecting the wave's properties.