A passenger car traveling due east at 53.6 m/s passes a truck traveling due east at 13.4 m/s.After the car passes,the horn on the truck is blown at a frequency of 350 Hz.The speed of sound in air is 335 m/s.The frequency heard by the driver of the car is
A)290 Hz
B)306 Hz
C)314 Hz
D)400 Hz
E)434 Hz

Question

Quizplus · Accepted Answer

The frequency heard by the driver of the car can be calculated using the Doppler effect formula for sound. Since the source (truck) and the observer (car) are moving in the same direction, the formula to use is: $f' = f \times \frac{v + v_o}{v + v_s}$, where $f'$ is the observed frequency, $f$ is the source frequency, $v$ is the speed of sound, $v_o$ is the speed of the observer, and $v_s$ is the speed of the source. Plugging in the given values: $f' = 350 \times \frac{335 + 53.6}{335 + 13.4}$, which gives an observed frequency of approximately 306 Hz.

A Passenger Car Traveling Due East at 53