If at the rate at which a disturbence is made is doubled, what what is the effect on the period, frequency, amplitude, and wavelength of a wave?

by definition, frequency is the rate at which disturbance is made through a medium. hence when rate at which disturbance is made doubled, the frequency also gets doubled,

Time period is given as

T = 1/f where T = time period, f = frequency

so when frequency is doubled, Time period becomes half, since Time period is inversely related to the frequency.

Amplitude does not depend on frequency hence amplitude remains unchanged.

wavelength is given as

λ = v/f

Wavelength becomes half when the frequency is doubled since wavelength is inversely related to frequency and speed is constant.