Final answer:
The beat frequency heard by the observer is the absolute difference between the frequencies of the two sources, represented by the equation fB = |f1 - f2|. This phenomenon creates an audible fluctuation in the sound when the sources have closely matched frequencies.
Step-by-step explanation:
The beat frequency heard by the observer when they listen from position A, in front of the car, is given by the absolute difference between the frequencies of the two sources. Therefore, the mathematical representation of the beat frequency is fB = |f1 - f2|, where f1 and f2 are the frequencies of the two sound sources. In the context of two cars moving towards each other with different frequencies, if an observer is positioned in front of one car, they would perceive a beat frequency that fluctuates in amplitude at this rate, given by the simple subtraction of the two different frequencies.
In the case of two tuning forks or car horns moving in opposite directions, the beat frequency would be the absolute difference in the observed frequencies after the Doppler shift has occurred due to their relative velocities. This phenomenon is noticeable when the frequencies of both sources are close together, resulting in an audible fluctuation or 'wobble' in sound volume and pitch known as beats.