The bicyclist hears a frequency of 417 Hz, which is lower than the original frequency of 440 Hz. This indicates that the bicyclist is behind the car.
When a car's horn sounds the note A (440 Hz) at rest, the frequency of the sound waves emitted by the horn remains constant. However, when the car is in motion, the frequency heard by an observer depends on their relative motion with respect to the car.
In this scenario, the bicyclist is moving in the same direction as the car but with one-eighth the car's speed. The frequency heard by the bicyclist is 417 Hz, which is lower than the original frequency of 440 Hz. This phenomenon is known as the Doppler effect.
The Doppler effect occurs because the motion of the source (the car) and the observer (the bicyclist) affects the perceived frequency of sound waves. When the source and the observer are moving towards each other, the observed frequency is higher than the emitted frequency. Conversely, when the source and the observer are moving away from each other, the observed frequency is lower than the emitted frequency.
In this case, since the frequency heard by the bicyclist is lower than the original frequency, it means that the bicyclist is behind the car. The bicyclist hears a lower frequency because the sound waves emitted by the car are "stretched" as they travel towards the bicyclist due to the relative motion of the two objects.