You blow a whistle of f=909 Hz as you move towards a wall. The fbeats you hear from the whistle is 14beats/second. How fast are you moving towards the wall?
To determine how fast you are moving towards the wall, we can use the formula for the frequency of sound perceived by a moving observer:
f observed = (f source * (v sound + v observer)) / (v sound)
In this formula:
- f observed is the frequency of the sound heard by the observer.
- f source is the frequency of the sound emitted by the source (blown whistle).
- v sound is the speed of sound.
- v observer is the velocity of the observer (your speed).
Here, we are given:
- f source = 909 Hz (frequency of the whistle)
- f beats = 14 beats/second (frequency of the beats)
- v sound = speed of sound (approximately 343 meters/second)
Since the frequency of beats is the difference between the observed frequency and the source frequency, we can write:
f beats = f observed - f source
Let's solve for the value of f observed:
f beats = f observed - f source
14 beats/second = f observed - 909 Hz
Now, let's calculate the frequency observed as a result of the Doppler effect:
f observed = f beats + f source
f observed = 14 beats/second + 909 Hz
f observed ≈ 923 Hz
With f observed known, we can now calculate your velocity (v observer) using the Doppler effect formula:
f observed = (f source * (v sound + v observer)) / (v sound)
Rearranging the formula to solve for v observer:
v observer = ((f observed / f source) - 1) * v sound
Plugging in the known values:
v observer = ((923 Hz / 909 Hz) - 1) * 343 m/s
v observer ≈ 16.2 m/s
Therefore, you are moving towards the wall at a speed of approximately 16.2 meters per second.