At rest, a car’s horn sound at the note A(440Hz) The horn is sounded while the car is moving down the street. A bicyclist moving the same direction with one third the car’s speed hears a frequency of 415 Hz. What is the speed of the car? Is the cyclist adead of or behind the car?
The car is behind the cyclist, and moving closer, the pitch is higher.
use the speed of the source (car) as v, and that of the observer (moving away) as 1/3 v.
Use the doppler equatin. I will be happy to check your work.
To determine the speed of the car, we can use the Doppler effect equation. The equation relates the observed frequency (f') to the source frequency (f) and the relative speeds of the source and observer.
The Doppler effect equation for frequency is given by:
f' = f * (v + vo) / (v - vs)
Where:
f' is the observed frequency
f is the source frequency (440 Hz)
v is the speed of sound in air (approximately 343 m/s at room temperature)
vo is the velocity of the observer (in this case, the cyclist) relative to the medium (air)
vs is the velocity of the source (in this case, the car) relative to the medium (air)
Given that the observed frequency is 415 Hz and the velocity of the observer (cyclist) is 1/3 the velocity of the source (car), we can plug these values into the equation:
415 = 440 * (343 + (1/3)*vo) / (343 - vs)
We also need to consider the signs in the equation. Since the car is moving closer to the cyclist, the velocity of the source (vs) will be negative. Similarly, since the cyclist is moving in the same direction as the car, the velocity of the observer (vo) will also be negative.
Now we can solve this equation for the speed of the car (vs).