No, the wavelength of a wave does not become shorter in shallow water. In fact, the wavelength remains the same as long as the wave is in the same medium (in this case, water). However, the speed of the wave changes in shallow water, which can affect other properties of the wave.
When a wave travels from deep water to shallow water, its speed decreases because the depth of the water is reduced. According to the principle of conservation of energy, since the wave speed decreases, the wavelength must also decrease to compensate and maintain a constant frequency.
As the wave moves into shallower water, the wavefronts start to "bunch up" because the wave is traveling slower. This can create the appearance of shorter wavelengths, but in reality, it is the same wavelength compressed into a smaller distance. The actual length of the wave itself remains the same.
It's important to note that this change in wave behavior occurs when the depth of the water becomes comparable to or smaller than the wavelength of the wave. In deep water where the depth is much greater than the wavelength, the wave behaves differently and the wavelength remains relatively constant.