The wavelength of a wave is determined by its frequency and the speed of propagation. Doubling the amplitude and frequency while keeping the time period constant does not directly affect the speed of propagation. Therefore, the wavelength will remain the same.
The formula relating the wavelength (λ), frequency (f), and speed of propagation (v) is:
λ = v / f
Since the speed of propagation remains constant and the time period (T) is inversely proportional to the frequency (f), the formula can be rewritten as:
λ = v * T
Since the time period is constant, the wavelength will also remain constant in this scenario.