When the frequency of a wave is constant, the relationship between wavelength and amplitude depends on the type of wave. There are two main types of waves: transverse waves and longitudinal waves.
Transverse Waves: In a transverse wave, the particles of the medium oscillate perpendicular to the direction of wave propagation. Examples of transverse waves include electromagnetic waves (such as light) and waves on a string. In transverse waves, the amplitude and wavelength are independent of each other. Changing the amplitude does not affect the wavelength, and changing the wavelength does not affect the amplitude. So, when the frequency is constant, the wavelength and amplitude can vary independently.
Longitudinal Waves: In a longitudinal wave, the particles of the medium oscillate parallel to the direction of wave propagation. Examples of longitudinal waves include sound waves and seismic waves. In longitudinal waves, there is a relationship between wavelength and amplitude when the frequency is constant. Specifically, the amplitude of a longitudinal wave is related to the compression and rarefaction of the wave. Compression refers to the regions of high pressure or density, while rarefaction refers to the regions of low pressure or density. In general, as the wavelength of a longitudinal wave increases, the amplitude also tends to increase. This means that longer wavelength longitudinal waves typically have larger amplitudes, and shorter wavelength longitudinal waves have smaller amplitudes, when the frequency remains constant.
It's important to note that the specific relationship between wavelength and amplitude in a longitudinal wave can be influenced by various factors, such as the source of the wave or the properties of the medium through which it propagates. However, in a general sense, the above description holds true.