In a transverse wave, the displacement of the medium occurs perpendicular to the direction of wave propagation. If the amplitude remains the same but the wavelength doubles, the wave will appear stretched out or elongated compared to its original form.
Let's consider an example of a transverse wave on a string. Initially, if the wave has a certain wavelength and amplitude, it might look like a series of peaks and troughs at regular intervals, with the amplitude representing the maximum displacement from the equilibrium position.
If the wavelength of the wave doubles while the amplitude remains the same, the peaks and troughs will become more spread out. The distance between consecutive peaks or troughs will be twice as large as before. This stretching out of the wave is a result of the increase in wavelength.
However, it's important to note that the amplitude remains unchanged, so the height of the peaks or depth of the troughs will remain the same. The wave will simply become more spaced out, with a longer distance between each peak and trough.
Visually, the wave would appear to have a lower frequency since the number of peaks and troughs passing a given point per unit time decreases. The wave will have a longer wavelength but the same amplitude as before.