Two cars drive along the same road towards each other, one
at 15 m/s and the other at 12 m/s. Each car horn sounds at
256 Hz. Calculate the frequency that the driver of each car
hears coming from the other car
To calculate the frequency that each driver hears coming from the other car, we need to consider the Doppler effect. The Doppler effect is the change in frequency or wavelength of a wave as observed by an observer moving relative to the source of the wave. In this case, the source of the sound wave is the car horn, and the observer is the driver in the other car.
First, let's find the relative speed between the two cars. Since they are driving towards each other, the relative speed is the sum of the speeds of the two cars:
Relative speed = Speed of Car 1 + Speed of Car 2
Relative speed = 15 m/s + 12 m/s
Relative speed = 27 m/s
Next, we can use the formula for the Doppler effect to calculate the frequency observed by the other driver:
Observed frequency = (Speed of sound + Relative speed) / (Speed of sound) * Source frequency
The speed of sound is approximately 343 m/s.
Observed frequency = (343 m/s + 27 m/s) / (343 m/s) * 256 Hz
Observed frequency = 370/343 * 256 Hz
Observed frequency ≈ 277.5 Hz
Therefore, the driver of each car would hear a frequency of approximately 277.5 Hz coming from the other car.