Final answer:
Doubling the tension on a string affects the wave speed, but does not directly change the amplitude, angular frequency, or wave number. The increase in speed will affect the wavelength if the frequency is kept constant. The correct option is D. None of the above.
Step-by-step explanation:
If the tension on a string is doubled while the student is whipping the string at a constant rate, the amplitude of the wave (A), the angular frequency (ω), and wave number (k) will not change directly as a result of this adjustment in tension. Instead, changing the tension primarily affects the wave speed on the string. However, the amplitude could be indirectly affected if there is a change in the way the wave is generated due to the tension change.
For a wave on a string, the speed (v) can be calculated using the formula v = √(T/μ), where T is the tension and μ is the linear mass density. Doubling the tension results in the wave speed increasing by the square root of two. Keeping the frequency constant means that the wavelength will now be longer due to the increased speed by the relationship v = fλ where v is the wave speed, f is the frequency, and λ is the wavelength.
The correct option for the change when the tension is doubled is D. None of the above. Amplitude, the angular frequency, and wave number are properties determined by the source of the wave and the medium, so they are generally not affected by the tension of the string in the context provided.