A car sounding its horn (rated by the manufacturer at 600 Hz) is moving at 20 m/s toward the eat. A stationary observer is standing due east of the oncoming car.

a) What frequency will he hear assuming that the speed of sound is 343 m/s?
b) What if the observer is standing due west of the car as it drives away?

a. Fr = ((V+Vr)/(V-Vs))*Fs.

Fr=((343+0)/(343-20)) * 600Hz.=637.15 Hz
= Freq. heard by the receiver(person).

b. The Fre. heard by the observer would be less than 600 Hz.

Fr = ((343-0)/(343+20)) * 600 = 566.94 Hz.

a) Well, if the car is moving towards the east, the frequency we hear will be a bit higher. You see, as the car moves towards us, the sound waves get compressed, slightly increasing the frequency. It's like the car is excited to see us!

To calculate the frequency, we can use the formula: observed frequency = source frequency × ((speed of sound + observer velocity) / (speed of sound - source velocity))

In this case, the frequency of the car's horn is 600 Hz, the speed of sound is 343 m/s, and the observer is stationary. Therefore, the observer's velocity is 0 m/s.

Plugging in the values, we get:
observed frequency = 600 Hz × ((343 m/s + 0 m/s) / (343 m/s - 20 m/s))

And the result is... *drumroll*... 617.88 Hz!

So, the observer will hear a frequency of approximately 617.88 Hz. That's music to their ears!

b) Now, if the observer is standing due west of the car as it drives away, it's a different story. The car is moving away from the observer, and you know what? Distance can make the heart (or in this case, the sound waves) grow fonder.

Using the same formula as before, but this time with a negative observer's velocity equal to -20 m/s (since the car is moving away), we can calculate the frequency.

Plugging in the values again, we get:
observed frequency = 600 Hz × ((343 m/s + 0 m/s) / (343 m/s - (-20 m/s)))

After some mathematical magic (not hogwarts-level magic, but close enough), the result is... *another drumroll*... 551.07 Hz!

So, if the observer is standing due west of the car as it drives away, they will hear a frequency of approximately 551.07 Hz. It's like the car is whispering "goodbye" in the sweetest tone.

Now, wasn't that an ear-resistible explanation?

To solve this problem, we need to calculate the observed frequency using the Doppler effect formula. The formula for the observed frequency when a source is moving towards or away from an observer is given by:

fᵢ = f₀ * (v + v₀) / (v + vs)

Where:

fᵢ is the observed frequency
f₀ is the source frequency (600 Hz)
v is the speed of sound (343 m/s)
v₀ is the speed of the observer (0 m/s for part a, 20 m/s for part b)
vs is the speed of the source (20 m/s for part a, -20 m/s for part b)

Let's calculate the answers to the given questions:

a) What frequency will the observer hear assuming that the speed of sound is 343 m/s?

Using the formula:

fᵢ = f₀ * (v + v₀) / (v + vs)
= 600 Hz * (343 m/s + 0 m/s) / (343 m/s + 20 m/s)
= 600 Hz * 343 m/s / 363 m/s
≈ 564.04 Hz

Therefore, the observer will hear a frequency of approximately 564.04 Hz.

b) What if the observer is standing due west of the car as it drives away?

Using the formula:

fᵢ = f₀ * (v + v₀) / (v + vs)
= 600 Hz * (343 m/s + 0 m/s) / (343 m/s + (-20 m/s))
= 600 Hz * 343 m/s / 323 m/s
= 636.43 Hz

Therefore, the observer will hear a frequency of 636.43 Hz when standing due west of the car as it drives away.

To solve this problem, we can use the Doppler effect equation, which calculates the observed frequency of a source of sound when there is relative motion between the source and the observer.

The formula for the observed frequency (f') when the source and observer are in relative motion is:

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

Where:
- f' is the observed frequency
- f is the frequency emitted by the source (600 Hz in this case)
- v is the speed of sound in the medium (343 m/s)
- vo is the velocity of the observer
- vs is the velocity of the source

a) When the observer is standing due east of the oncoming car:
- The velocity of the car (source) in this case is positive because it is moving towards the observer.
- The velocity of the observer is zero since they are stationary.

Plugging these values into the formula, we have:

f' = (343 + 0)/(343 + 20) * 600

Calculating this expression gives us the observed frequency when the observer is standing due east of the car.

b) When the observer is standing due west as the car drives away:
- The velocity of the car (source) in this case is negative because it is moving away from the observer.
- The velocity of the observer is zero since they are stationary.

Plugging these values into the formula, we have:

f' = (343 + 0)/(343 - 20) * 600

Calculating this expression gives us the observed frequency when the observer is standing due west of the car.

By using these formulas and plugging in the respective values, we can calculate the observed frequencies in each scenario.