Final answer:
Doubling the wavelength on a string halves the wavenumber while the phase velocity, period, and amplitude of the wave remain unchanged provided that the tension and linear mass density of the string are constant.
Step-by-step explanation:
If you double the wavelength on a string, the following changes occur:
- A. The phase velocity stays the same because velocity is determined by the tension and linear mass density of the string, which are assumed to be constant.
- B. The wavenumber, which is the spatial frequency of the wave and is defined as 2π divided by the wavelength, is halved since it is inversely proportional to the wavelength.
- C. The period of the wave remains constant assuming the frequency does not change.
- D. The amplitude of the wave is not affected by the change in wavelength; it remains the same unless an external factor influences it.