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When dealing with sound waves, understanding frequency change is crucial especially in the context of the Doppler Effect. The frequency observed by a listener differs from the source frequency due to relative motion. This phenomenon is essentially because of varying distances covered by successive sound waves.
For instance, when a sound source moves closer to an observer, the waves are compressed, leading to a higher frequency or pitch. Conversely, if the source moves away, the waves are stretched, causing a lower frequency. This is analogous to the perception of pitch for an approaching versus receding siren.
In the exercise, the train blowing a horn has an emitted frequency of 124 Hz. The observer on the second train hears this frequency as 135 Hz, a higher value due to both trains moving towards one another. The central concept here is the change in frequency due to relative motion.

Sound waves are disturbances that travel through a medium, such as air, in the form of longitudinal waves, where particles oscillate parallel to the wave direction. These vibrations cause areas of compression and rarefaction, enabling sound to propagate.
Each sound wave has characteristics such as frequency, wavelength, and speed, all interdependent. In this scenario, the frequency is altered by the movement of trains, highlighting how motion affects wave properties despite the speed of sound in air remaining relatively constant at around 343 m/s.
It's essential to understand that as long as the source or observer moves, the perceived frequency changes, not the wave speed. In our problem, the Doppler Effect explains the change in frequency while the sound wave's speed remains constant.

Relative motion, a fundamental concept in physics, describes how one body moves in relation to another. In the Doppler Effect, it's the relative speeds of the source and observer that provoke frequency changes. Relative motion is integral in determining the perceived direction and magnitude of frequency shifts.
In the Doppler Effect formula, each variable accounts for these relative movements. For example, in our exercise, the speed of the source train effectively alters the frequency heard by the observer on the second train, due to them both moving in the same direction, albeit at different speeds.
By determining the observer's speed, which was approximately 71.3 m/s in the problem, we see how relative motion affects the sound heard, exemplifying why shifts occur as objects approach one another. The faster the listener approaches the sound source, the greater the increase in frequency.