The amplitude of sound and mechanical waves does not directly influence the Doppler effect. The Doppler effect concerns the change in frequency or wavelength due to the relative motion between the source and observer. The amplitude, on the other hand, relates to the wave’s energy or intensity. However, it's worth noting that a higher amplitude can make the changes in frequency more discernible to observers in practical scenarios, especially in sound waves, where amplitude correlates with loudness. Thus, while amplitude doesn’t alter the frequency change induced by the Doppler effect, it can impact the ease with which this effect is observed and measured.

Wave intensity is crucial in observing the Doppler effect as it affects the observer’s ability to perceive frequency changes. Intensity refers to the power per unit area carried by a wave, impacting how ‘loud’ or ‘quiet’ a sound wave might be perceived, or how ‘strong’ or ‘weak’ a mechanical wave appears. While the Doppler effect influences the frequency or pitch of the sound, the intensity affects the amplitude or loudness. In scenarios with low-intensity waves, the Doppler effect might be more challenging to observe audibly or measure accurately, underscoring intensity as a significant factor in practical applications and observations.

The Doppler effect's principles are applicable to seismic waves, aiding in understanding Earth’s internal structures and predicting natural disasters like earthquakes. When seismic waves emanate from an earthquake’s epicentre, the wave frequencies change due to the Earth’s rotational motion, which can be understood through the Doppler effect. By analysing these frequency changes, seismologists can ascertain vital information about the earthquake’s location, depth, and energy release. This data is instrumental in enhancing predictive models, improving early warning systems, and fostering a deeper comprehension of geophysical processes governing the Earth’s dynamic activities.

The medium significantly impacts the Doppler effect by determining the speed at which waves travel. For sound and mechanical waves, variations in the medium’s properties, like temperature, pressure, and density, can alter wave speed. For instance, sound waves travel faster in warmer air compared to colder air due to the increased energy of air particles. This variation in wave speed affects the observed frequency changes associated with the Doppler effect. Hence, understanding the medium’s properties is essential for accurately predicting and calculating observed frequencies in various scenarios involving sound and mechanical waves.

Yes, the Doppler effect can be observed with both transverse and longitudinal mechanical waves. The key factor is the relative motion between the source and observer. For transverse waves, where particles of the medium move perpendicular to the direction of wave propagation, and longitudinal waves, where particles move parallel to the wave direction, the Doppler effect manifests as a change in observed frequency resulting from the source or observer’s motion. The mathematical principles and formulas for calculating these changes remain consistent, with adjustments made for the specific wave speeds and characteristics of different types of mechanical waves.