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Sound frequency refers to the number of sound wave vibrations that occur per second. It's measured in hertz (Hz), with one Hz equating to one vibration per second. In the context of the Doppler Effect, the original frequency of the sound source can change based on the movement of the source relative to an observer. This phenomenon is what leads us to shift from the original frequency to an apparent frequency that the observer hears. Understanding sound frequency is crucial in various fields like acoustics, music, and even medical imaging. In this exercise, the initial sound frequency of the horn is 800 Hz, which changes due to the relative motion between the two cars.

Converting units is vital in physics to ensure all calculations are in the correct units. For speed, it's common to convert from kilometers per hour (km/h) to meters per second (m/s), as the latter is the standard SI unit for velocity. The conversion factor is straightforward: 1 km/h is equivalent to \( \frac{1}{3.6} \text{ m/s} \). For example, if a car travels at 108 km/h, in meters per second, it's moving at 30 m/s once converted. Similarly, a car moving at 72 km/h is traveling at 20 m/s. This conversion is a critical first step in solving problems involving movement and velocity, such as applying the Doppler Effect to determine apparent frequencies.

Apparent frequency is the frequency heard by an observer and may differ from the original frequency due to the Doppler Effect. This occurs because the movement of the sound source and/or observer changes the wavelengths reaching the observer. When both source and observer move, as in this exercise, the formula to find the apparent frequency is \[ f' = f \left( \frac{v + v_o}{v + v_s} \right) \], where \( f \) is the original frequency, \( v \) is the speed of sound, \( v_o \) is the speed of the observer, and \( v_s \) is the speed of the source. For our exercise, substituting the respective speeds and frequency (800 Hz), gives an apparent frequency calculation that yields approximately 778 Hz.

The speed of sound is a constant that varies slightly depending on the medium through which it's traveling. In air, it's commonly taken to be 330 m/s at room temperature. This constant is used in calculations involving the Doppler Effect, where sound waves travel from the source to the observer. A faster speed of sound would result in lower apparent frequency shifts, while a slower speed could result in higher shifts. When calculating the apparent frequency, knowing the correct speed of sound aids in accurately applying the Doppler formula. In this scenario, we used 330 m/s as the speed of sound, which helped in deriving the accurate apparent frequency heard by the observer.