If you increase or decrease the amplitude of a wave while keeping the frequency constant, the wavelength of the wave remains unchanged. The wavelength of a wave is determined by its frequency and speed, 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
When you alter the amplitude of a wave without changing its frequency, you are adjusting the wave's maximum displacement or height while keeping the distance between successive wave cycles the same. This modification does not affect the relationship between frequency and wavelength, so the wavelength remains constant.
For example, imagine a sinusoidal wave with a certain frequency and wavelength. If you increase or decrease the amplitude of this wave, the distance between successive peaks or troughs does not change. The wave simply becomes taller or shorter, but the number of complete wave cycles per unit distance remains the same.
It's important to note that changing the amplitude of a wave without altering its frequency does not affect its speed or wavelength. The speed of a wave depends on the medium through which it travels and remains constant unless the medium changes.