If the amplitude of a transverse wave remains the same but the wavelength doubles, the wave's overall appearance will change. Let's understand how this affects the wave's characteristics:
Amplitude: The amplitude of a wave represents the maximum displacement of particles from their equilibrium position. It determines the wave's intensity or strength. If the amplitude remains the same, the wave's peaks and troughs will still have the same height from the equilibrium position.
Wavelength: The wavelength is the distance between two consecutive points in the wave that are in phase (e.g., two adjacent peaks or troughs). It determines the spatial extent of one complete cycle of the wave. If the wavelength doubles, it means that the distance between two consecutive peaks or troughs will become twice as long.
Frequency: The frequency of a wave is the number of complete cycles it completes in one unit of time. It is inversely proportional to the wavelength. If the wavelength doubles, the frequency will decrease by half (assuming the wave's speed remains constant).
So, what does this mean visually?
When the wavelength doubles, the wave will "stretch out" along the propagation direction, making it more spread out. The distance between peaks and troughs will be larger. However, the peaks and troughs will still have the same height, as the amplitude remains constant.
In summary, the transverse wave with a doubled wavelength will have a lower frequency (since frequency is inversely proportional to wavelength) and a more stretched-out appearance compared to the original wave, but its amplitude remains the same.