A CAR IS TRAVELING AWAY FROM YOU AT 70.0 MI/H. THE CAR HORN PRODUCES A SOUND AT A FREQUENCY OF 5000HZ. WHAT FREQUENCY DO YOU HEAR?

f =f(o)•(1-v/V) =5000•(1- 31.3/331.3)= =4528 Hz

v =70 mph = 31.3 m/s
V =331,3 m/s (speed of sound)

f =f(o)•(1+v/V) =5000•(1+ 31.3/331.3)= =5472 Hz

v =70 mph = 31.3 m/s
V =331,3 m/s (speed of sound)

I believe you understand that the first solution is for the motion away from you, and the second solution is for the motion towards you.

To determine the frequency you hear, we need to consider the Doppler effect. The Doppler effect is the change in frequency or pitch of a sound wave due to the relative motion between the source of the sound and the observer.

In this case, the car is traveling away from you. When a source of sound is moving away, the frequency of the sound waves appears to decrease to the observer.

The formula to calculate the frequency you hear is given by:

f' = f * (v + v_o) / (v + v_s)

Where:
f' represents the frequency you hear,
f represents the frequency of the car horn (5000 Hz in this case),
v represents the speed of sound (which is approximately 343 m/s),
v_o represents the velocity of the observer (in this case, it's 0 m/s since you are stationary), and
v_s represents the velocity of the source (70.0 mi/h converted to m/s).

Let's calculate the frequency you hear:

1. Convert the velocity of the car from miles per hour to meters per second:
V_s = (70.0 mi/h) * (1.60934 km/mi) * (1000 m/km) / (3600 s/h) ≈ 31.29 m/s

2. Substitute the values into the formula:
f' = 5000 Hz * (343 m/s + 0 m/s) / (343 m/s + 31.29 m/s)

3. Simplify the equation:
f' = 5000 Hz * 343 m/s / 374.29 m/s ≈ 4577 Hz

Therefore, you would hear a frequency of approximately 4577 Hz.