In a longitudinal wave, such as a sound wave, the motion of particles of the medium is parallel to the direction of wave propagation. The amplitude of a wave refers to the maximum displacement of particles from their equilibrium position as the wave passes through the medium.
When the amplitude of a longitudinal wave changes, it does not affect the wavelength because the wavelength is determined by the source of the wave or the frequency at which it is produced. The wavelength represents the distance between two consecutive points of the wave that are in phase, such as two compressions or two rarefactions in the case of a sound wave.
The change in amplitude affects the intensity or energy carried by the wave, but it does not alter the distance between consecutive points of the wave that are in phase. As long as the frequency remains constant, the wavelength remains unchanged. This is because the frequency of the wave determines how quickly the compressions and rarefactions follow each other, while the amplitude determines the maximum displacement of the particles from their equilibrium position.
In summary, the wavelength of a longitudinal wave is determined by the frequency of the wave and is not affected by changes in the amplitude.