a car, moving at 100 mi/hr, passes a stationary police car whose siren has a frequency of 500 Hz. what is the frequency change heard by observer in the moving car as he passes the police car? the velocity of sound in air is 343 m/s. ( 1 mi= 1.609 km).

answer in units of Hz.

To find the frequency change heard by the observer in the moving car, we can use the Doppler effect formula:

Δf = ((v + vo) / v) * fo - fo

Where:
Δf = Frequency change
v = Velocity of sound in air (343 m/s)
vo = Velocity of the observer (moving car) relative to the sound source (police car)
fo = Original frequency emitted by the sound source (500 Hz)

First, we need to convert the velocity of the moving car from miles per hour to meters per second and the conversion factor is 1.609 km = 1 mile.

So, 100 miles/hour = 100 * 1.609 km/hour = 160.9 km/hour.
Converting km/hour to m/s, we divide by 3.6 (since there are 3600 seconds in an hour):
160.9 km/hour / 3.6 = 44.6983 m/s.

Now we have the velocity of the moving car (vo) relative to the sound source (police car), which is approximately 44.6983 m/s.
Substituting these values into the Doppler effect formula:

Δf = ((v + vo) / v) * fo - fo
Δf = ((343 + 44.6983) / 343) * 500 - 500

Calculating this, we find:

Δf ≈ (387.6983 / 343) * 500 - 500
Δf ≈ 1.130 * 500 - 500
Δf ≈ 565 - 500
Δf ≈ 65 Hz

Therefore, the frequency change heard by the observer in the moving car as he passes the police car is approximately 65 Hz.

To find the frequency change heard by the observer in the moving car, we can use the Doppler effect formula:

Δf/f₀ = v/343

Where:
Δf is the change in frequency
f₀ is the original frequency (500 Hz)
v is the velocity of the moving car relative to the observer (in this case, the police car)

First, we need to convert the speed of the moving car from miles per hour to meters per second:
100 mi/hr * 1.609 km/mi * 1000 m/km * 1 hr/3600 s = 44.7 m/s

Now let's substitute the values into the formula:
Δf/500 Hz = 44.7 m/s / 343 m/s

To find the change in frequency (Δf), we can rearrange the formula:

Δf = (44.7 m/s / 343 m/s) * 500 Hz

Calculating the above expression, we get:
Δf ≈ 0.652 Hz

Therefore, the frequency change heard by the observer in the moving car as he passes the police car is approximately 0.652 Hz.

Vr=100mi/h * 1609m/mi * (1h/3600s)=44.69m/s.

F = ((V-Vr)/(V+Vs))*Fo.
F=((343-44.69) / (343+0))*500 = 434.9Hz

Change = 500 - 433.9 = 65.1Hz.