A car drives at a speed of 28m/s along a road parallel to a railroad track. A train traveling at 15m/s sounds a horn that vibrates at 300 Hz.
If the train and car are moving toward each other, what frequency of sound is heard by a person in the car?
If the train and car are moving away from each other, what frequency of sound is heard in the car?
Isn't there a standard formula for this?
https://www.google.com/search?q=doppler+formula&ie=utf-8&oe=utf-8
To calculate the frequency heard by a person in the car, we need to take into account the Doppler effect. The Doppler effect is the change in frequency of a wave (such as sound or light) due to the relative motion between the source and the observer.
1. When the train and car are moving toward each other:
In this case, the observer (person in the car) is stationary, and the source (train) is moving towards them. The observed frequency will be higher than the actual frequency of the source.
The formula to calculate the observed frequency when the observer is at rest is as follows:
f' = (v + vo) / (v - vs) * f
Where:
f' is the observed frequency
f is the actual frequency of the source
v is the speed of sound in air (approximately 343 m/s)
vo is the velocity of the observer (in this case, the car)
vs is the velocity of the source (in this case, the train)
Given:
f = 300 Hz
vo = 28 m/s (since the car is moving at 28 m/s)
vs = 15 m/s (since the train is moving at 15 m/s)
v = 343 m/s
Plugging the values into the formula:
f' = (v + vo) / (v - vs) * f
f' = (343 + 28) / (343 - 15) * 300
Calculating:
f' ≈ 326.13 Hz
Therefore, when the train and car are moving toward each other, a person in the car would hear a frequency of approximately 326.13 Hz.
2. When the train and car are moving away from each other:
In this case, the observer (person in the car) is stationary, and the source (train) is moving away from them. The observed frequency will be lower than the actual frequency of the source.
Using the same formula as above:
Given:
f = 300 Hz
vo = 28 m/s
vs = -15 m/s (since the train is moving away)
v = 343 m/s
Plugging the values into the formula:
f' = (v + vo) / (v - vs) * f
f' = (343 + 28) / (343 - (-15)) * 300
Calculating:
f' ≈ 274.03 Hz
Therefore, when the train and car are moving away from each other, a person in the car would hear a frequency of approximately 274.03 Hz.