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

Well, let me set the scene for you. We have a train and a car having a little race on a highway. The train is moving at a speed of 23 m/s because, well, it's a train and trains are kind of slow. The car, on the other hand, is feeling a bit more ambitious and goes zooming by at 46 m/s.

Now, here comes the interesting part. The car is behind the train and its driver’s ears are itching to hear that awesome train whistle. The train whistle is normally at a frequency of 360 Hz, but because of the relative motion between the car and the train, things start getting a bit wonky.

Since the car is moving faster than the train, the sound waves from the whistle have a harder time catching up with the car. It's like the train is telling the sound waves, "Hey, hurry up and catch that speedy car!" So, the sound waves get compressed a bit, resulting in a higher frequency observed by the car's occupant.

To figure out how much the frequency changes, we can use the formula for the Doppler effect, which takes into account the speeds of the objects and the speed of sound. Plugging in the numbers, we get:

Observed frequency = Actual frequency * (Speed of sound / (Speed of sound - Speed of car))

= 360 Hz * (343 m/s / (343 m/s - 46 m/s))

So, after chugging through the calculations (pun intended), we find that the occupant of the car will observe a frequency of approximately 402.73 Hz for the train whistle.

So, there you have it! The car's occupant will hear a woo-hoo-worthy frequency of about 402.73 Hz coming from the train whistle. Let's hope they enjoy the harmonious symphony of the highway!

To find the frequency observed by the car's occupant for the train whistle, we can use the Doppler effect equation:

f_observed = f_source * (v_sound + v_observer) / (v_sound + v_source)

Where:
f_observed is the observed frequency,
f_source is the source frequency,
v_sound is the speed of sound,
v_observer is the velocity of the observer (car),
and v_source is the velocity of the source (train).

Given:
f_source (train whistle) = 360 Hz,
v_sound = 343 m/s,
v_observer (car) = 46 m/s,
v_source (train) = 23 m/s (note: since the car is behind the train, we consider it a positive value).

Now, let's substitute the values into the formula:

f_observed = 360 * (343 + 46) / (343 + 23)

Simplifying the equation:

f_observed = 360 * 389 / 366

f_observed ≈ 383.94 Hz

Therefore, an occupant of the car will observe the train whistle at approximately 383.94 Hz.

To determine the frequency observed by an occupant of the car for the train's whistle, we need to consider the concept of the Doppler effect.

The Doppler effect is the change in frequency of a wave (in this case, sound) when there is relative motion between the source of the wave and the observer.

In this scenario, the car is moving with a higher velocity compared to the train, and both are moving in the same direction. Since the car is behind the train, the relative motion between them is given by the difference in their velocities: 46 m/s (car) - 23 m/s (train) = 23 m/s.

The next step is to apply the formula for the Doppler effect for sound:

f' = f * (v + vo) / (v + vs)

Where:
f' is the observed frequency,
f is the source frequency (original frequency of the whistle),
v is the speed of sound,
vo is the velocity of the observer (car),
vs is the velocity of the source (train).

Plugging in the given values:
f' = 360 Hz * (343 m/s + 46 m/s) / (343 m/s + 23 m/s)

Calculating this expression gives us:
f' = 360 Hz * 389 m/s / 366 m/s
f' ≈ 382.8 Hz

Therefore, an occupant of the car would observe a frequency of approximately 382.8 Hz for the train whistle.