91Ó°ÊÓ

The concept of frequency change is central to understanding the Doppler Effect. When two objects, like the trucks in our problem, are in relative motion toward each other, the frequency of the sound waves emitted by one truck's horn appears to increase for the driver of the other truck. This is because the waves are "bunched up" as they are encountered more frequently, leading to a higher observed frequency. In contrast, if the objects were moving apart, the sound waves would spread out, and the frequency would decrease.
In the context of this exercise, the observed frequency is 1.14 times the frequency when stationary, indicating that the sound waves are being compressed due to the trucks approaching each other.
This change in frequency does not mean the true frequency of the horn has altered; it results purely from the relative motion between the source and observer. This phenomenon allows us to calculate how fast the trucks are traveling by using the changes in sound wave frequency.

Sound waves are vibrations that propagate through air, or another medium, as acoustic waves. These waves have characteristics such as wavelength, speed, and frequency.
When discussing the Doppler Effect, understanding sound wave properties is crucial. The speed of sound is given as 343 m/s in the given problem. This speed contributes to how quickly the sound waves move from the source truck to the observer truck.
Sound frequency is the rate at which the waves pass a point and is measured in Hertz (Hz). In this problem, while the actual frequency of the horn is never directly stated, we know the observed frequency (the frequency heard by the other truck's driver) is amplified by a factor of 1.14. This increase is a result of sound waves compressing as both trucks move toward each other.

Relative motion describes how an observer's motion regarding the motion of the source affects the perception of various physical phenomena, like sound waves in our exercise.
For our trucks, relative motion is key because both trucks are moving towards each other, which influences how the driver perceives the horn's frequency. If the trucks were stationary or moving apart, the frequency experienced by the driver would differ significantly.
In this problem, applying the relative motion concept allows us to use the Doppler Effect formula to establish a relationship between observed frequency, speed of sound, and trucks' speeds. By rearranging the formula \[ f' = \frac{f(v + v_o)}{v - v_s} \] we capture the interaction of these factors. With the given frequency change and known speed of sound, we solve for the trucks' speed, illustrating the powerful role of relative motion in modifying perceived sound.