A train is moving parallel and adjacent to a highway with a constant speed of 23 m/s. A car is traveling in the same direction as the train at 46 m/s. The car’s horn sounds at 550 Hz and the train’s whistle sounds at 360 Hz. When the car is behind the train what fre- quency does an occupant of the car observe for the train whistle? The speed of sound is 343 m/s. Answer in units of Hz (part 2 of 2) When the car is in front of the train what frequency does a train passenger observe for the car’s horn? Answer in units of H

Isn't there a standard formula for this?

To calculate the frequency observed by an occupant in the car when the car is behind the train, we need to consider the concept of Doppler effect. The Doppler effect is the change in frequency of a wave (sound in this case) as the source of the wave (train or car) and the observer (car or train) move relative to each other.

When the car is behind the train, both the car and the observer (occupant in the car) are moving in the same direction. In this case, we use the following formula to calculate the observed frequency:

Observed frequency = Source frequency * (Speed of sound + Relative velocity between the source and observer) / (Speed of sound)

Here, the source frequency is 360 Hz (train's whistle), the speed of sound is 343 m/s, and the relative velocity between the train and the car can be calculated by subtracting the car's velocity from the train's velocity:

Relative velocity = Train velocity - Car velocity = 23 m/s - 46 m/s = -23 m/s

(Note that the negative sign indicates that the velocity is in the opposite direction.)

Plugging in the values into the formula:

Observed frequency = 360 Hz * (343 m/s - (-23 m/s)) / 343 m/s

Simplifying the expression:

Observed frequency = 360 Hz * (366 m/s) / 343 m/s

Observed frequency ≈ 384 Hz

Therefore, when the car is behind the train, an occupant in the car would observe the train whistle at a frequency of approximately 384 Hz.

Now, let's move on to the second part of the question: when the car is in front of the train, what frequency does a train passenger observe for the car's horn.

In this case, the train and the observer (train passenger) are moving towards each other. We use the same formula as before, but this time the relative velocity between the train and the car is the sum of their velocities:

Relative velocity = Train velocity + Car velocity = 23 m/s + 46 m/s = 69 m/s

Plugging in the values into the formula:

Observed frequency = Source frequency * (Speed of sound + Relative velocity between the source and observer) / (Speed of sound)

Observed frequency = 550 Hz * (343 m/s + 69 m/s) / 343 m/s

Simplifying the expression:

Observed frequency = 550 Hz * (412 m/s) / 343 m/s

Observed frequency ≈ 662 Hz

Therefore, when the car is in front of the train, a train passenger would observe the car's horn at a frequency of approximately 662 Hz.

I was absent on Thursday and school was canceled Friday due to ice... its due at 10pm