If you double both the frequency and amplitude of a monochromatic wave at the same time, the wavelength of the wave remains unchanged. The wavelength of a wave is determined by its frequency, and it is inversely proportional to the frequency.
The formula that relates the speed of a wave (v), its frequency (f), and its wavelength (λ) is:
v = f × λ
In this case, when you double the frequency (f) and amplitude of the wave while keeping the wavelength (λ) the same, the speed of the wave (v) remains constant. Since the speed of the wave is constant, the relationship between frequency and wavelength remains unchanged. Therefore, the wavelength remains the same.
It's important to note that changing the frequency and amplitude of a wave independently will have different effects on the wave's characteristics.