The Doppler effect is observable primarily in mechanical and electromagnetic waves. Mechanical waves, like sound, require a medium to travel through. In these waves, the effect is more pronounced because the speed of the waves, compared to the speeds of sources and observers, isn't exceedingly high. For electromagnetic waves, like light, which travel at the speed of light, the Doppler effect is still observable but requires highly sensitive equipment to detect the frequency changes, especially when the relative speeds are not close to the speed of light.

In astronomy, the Doppler effect is crucial for interpreting data from distant celestial bodies. Astronomers account for this effect by carefully analysing the spectral lines of stars and galaxies. Shifts in these spectral lines, either towards the blue or red end of the spectrum, indicate the velocity of the object relative to the Earth. By measuring the degree of this shift, astronomers can calculate the speed and direction of a star's motion. Corrections for the Doppler effect are integral to ensuring that the data on celestial objects' luminosity, composition, and other attributes are accurate.

Distinguishing between a Doppler shift due to motion and frequency changes from other factors requires careful analysis. For example, in the context of light waves, factors other than motion, such as gravitational redshift, can influence the observed frequency. Astronomers and physicists use additional data and contextual clues to make this distinction. In the case of sound waves, environmental factors like wind speed and direction, temperature, and humidity can also affect wave propagation and frequency. Thus, a comprehensive analysis considering all potential influencing factors is essential to isolate and accurately attribute observed frequency changes to the Doppler effect.

The motion direction of the source or observer is crucial in determining whether the observed frequency increases or decreases. When the source approaches the observer, the waves compress, leading to an increase in frequency, observed as a higher pitch in sound or a blue shift in light. Conversely, if the source is moving away, the waves spread out, causing a reduction in frequency, observed as a lower pitch or red shift. The observer’s motion has a similar effect; moving towards the source increases frequency and moving away decreases it.

The formulas used to calculate observed frequencies and velocities are theoretical models that provide approximations. In real-life scenarios, various factors can influence their accuracy. For instance, changes in the medium's properties, such as air density or temperature, can affect wave speed. Additionally, the relative speeds of the source and observer can impact the extent to which the Doppler effect is noticeable. Hence, while these formulas offer valuable insights and are generally reliable, they might not account for all variables encountered in complex real-world situations.