After giving an intense performance, a confused and disoriented flautist has wandered onto the motorway! They are playing a constant 300Hz on their flute and are essentially stationary If you are driving along the motorway at 100 km/h(27.8 m/s). What is the frequency you hear from the flautist's you hear from the flautist's instrument before you pass them and after you pass them?
This is also a part of it!!
Coincidently the horn on your car, which you sound as you narrowly miss the flautist in problem 1, also give a constant 300 Hz. tone. What frequency does the flautist hear before and after you pass them?
Toward:
fo = fs (1+vo/v)
away is minus instead of plus.
To determine the frequency you hear from the flautist's instrument before and after you pass them on the motorway, we need to consider the concept of 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 scenario, the observer is you, driving along the motorway at a constant speed of 100 km/h (27.8 m/s). The source of the sound is the flautist playing a constant 300 Hz note.
Before you pass the flautist:
As you approach the flautist, the relative motion between you and the source is from you toward the source. This causes the sound waves to be compressed, leading to a higher perceived frequency. The formula for this scenario is:
f' = (v + v₀) / (v - vₛ) * f₀
Where:
f' is the perceived frequency (in Hz)
v is the speed of sound in air (approximately 343 m/s)
v₀ is the speed of the observer (you)
vₛ is the speed of the source (flautist)
f₀ is the frequency of the source (flautist's playing frequency)
Plugging in the values:
v = 343 m/s
v₀ = 27.8 m/s
vₛ = 0 m/s (as the flautist is stationary)
f₀ = 300 Hz
f' = (343 + 27.8) / (343 - 0) * 300
f' = 1.0993 * 300
f' ≈ 329.79 Hz
Therefore, before you pass the flautist, you would hear a frequency of approximately 329.79 Hz.
After passing the flautist:
Once you have passed the flautist, the relative motion between you and the source is from you away from the source. This leads to the sound waves being stretched, resulting in a lower perceived frequency.
Using the same formula as before, plugging in the values:
v = 343 m/s
v₀ = 27.8 m/s
vₛ = 0 m/s (as the flautist is still stationary)
f₀ = 300 Hz
f' = (343 - 27.8) / (343 + 0) * 300
f' = 0.8659 * 300
f' ≈ 259.77 Hz
Therefore, after passing the flautist, you would hear a frequency of approximately 259.77 Hz.