A truck is moving away at 30 mph from a car moving towards the truck at 60 mph. If
the truck emits a horn of frequency 500 Hz, what frequency does the driver of the car hear to 3
significant digits?
how do i solve i know the answer is 519hz but how?
To solve this problem, we can use the formula for the Doppler effect. The Doppler effect describes the change in frequency of a wave (in this case, sound) as perceived by an observer moving relative to the source of the wave.
The formula for the observed frequency is:
f' = (v + vo) / (v - vs) * f
Where:
- f' is the observed frequency
- v is the speed of sound in air (which is approximately 343 meters per second)
- vo is the velocity of the observer (the driver of the car) relative to the medium (air) – positive if the observer is moving toward the source, negative if moving away
- vs is the velocity of the source (the truck) relative to the medium (air) – positive if the source is moving away, negative if moving toward the observer
- f is the original frequency emitted by the source (the truck's horn) – in this case, 500 Hz
Given that the truck is moving away at 30 mph and the car is moving towards the truck at 60 mph, we need to convert these velocities from miles per hour to meters per second:
30 mph = 13.4112 m/s (approximately)
60 mph = 26.8224 m/s (approximately)
Plugging these values into the formula:
f' = (343 + 13.4112) / (343 - 26.8224) * 500
= 519.037 Hz (approximately)
Therefore, the driver of the car hears a frequency of approximately 519 Hz.
the car is overtaking the truck
the relative speed is 30 mph
... the distance is closing
... that's why the Doppler frequency is higher
apparent frequency = actual frequency * [(speed of sound) / (speed of sound - closing speed)]