A car traveling 35.0 m/s overtakes another car going only 22.0 m/s. When the faster car is still behind the slower one, it sounds a horn of frequency 1500.0Hz. What is the frequency heard by the driver of the slower car?
What is the altitude of the plane?
Fo = ((Vs+Vo)/(Vs-Vh)*Fh.
Fo = ((343+22)/(343-35))*1500 - 1777.6 Hz.
Fo = Freq. heard by the observer(slower driver).
Vs = Speed of sound.
Vo = Speed of the observer(slower driver).
Vh = Speed of the horn(faster driver).
Fh = Freq. of the horn.
To calculate the frequency heard by the driver of the slower car, we can use the concept of the Doppler effect. The Doppler effect is the change in frequency or wavelength of a wave as observed by an observer moving relative to the source of the wave.
Step 1: Determine the velocity of sound
The velocity of sound is approximately 343 m/s in air at room temperature.
Step 2: Determine the velocities of the cars
Given that the first car is traveling at 35.0 m/s and the second car is going at 22.0 m/s, the relative velocity between the two cars is the difference between their speeds:
Relative velocity = 35.0 m/s - 22.0 m/s = 13.0 m/s
Step 3: Apply the Doppler effect formula
The Doppler effect formula for sound is given by:
f' = f * (v + v₀) / (v + vₛ)
Where:
f' = frequency heard by the observer (driver of the slower car)
f = frequency emitted by the source (horn)
v = velocity of sound
v₀ = velocity of the observer (driver of the slower car)
vₛ = velocity of the source (driver of the faster car)
Substituting the known values into the formula:
f' = 1500.0 Hz * (343 m/s + 0 m/s) / (343 m/s + 13.0 m/s)
f' = 1500.0 Hz * (343 m/s) / (356.0 m/s)
f' = 1442.91 Hz
Therefore, the frequency heard by the driver of the slower car is approximately 1442.91 Hz.
Now, moving on to the question about the altitude of the plane. Could you please provide more context or details about the scenario as it is difficult to answer without additional information?