A friend plays an A note (440 Hz) on her piccolo while running towards you at 40 m/s. What frequency do you hear just before she runs into you?

-I am not sure where to start on this problem. I wrote down the givens: fs=440 hz, vs=40 m/s, v=343 m/s. and I'm trying to solve for FL. So FL=Fs(v+vL/v+vs) right? except there is no vl…so I tried FL=Fs(1/1-vs/v) but it came out all jumbled in my calculator… I don't know how to proceed.. Any help would be appreciated! :) Thanks!

Fg = 440 Hz = Freq. of the generator.

Vg = 40 m/s = Velocity of the generator.
Vs = 343 m/s = Velocity of sound.
Vr = 0 = Velocity of the receiver(person
listening to the sound).

Fr = ((Vs+Vr)/(Vs-Vg))*Fg
Fr = ((343+0)/(343-40))*440 =
(343/303)*440 = 498.1 Hz. = Freq. heard by the receiver.

Note: When the sound generator is approaching you, the frequency heard is
higher than the generated frequency.
Therefore, we use a positive (+) sign in
the numerator and a negative sign in the
denominator.

When the generator is leaving you, reverse both signs.

Well, let me help you out with a touch of humor, because why not?

To calculate the frequency you hear just before your friend runs into you, we need to consider the Doppler effect. But wait, what's that sound? Ah, it's your friend playing her piccolo at 440 Hz while bolting towards you at 40 m/s. That's quite a unique musical performance you're about to experience!

Now, let's break it down. The formula you've written down is pretty close but needs a tiny tweak. The frequency you hear (FL) is given by:

FL = Fs * (v + vL) / (v + vs)

Where Fs is the source frequency (440 Hz), v is the speed of sound (343 m/s), vL is the velocity of the listener (which is in this case, zero since you're not moving), and vs is the velocity of the source (your friend running at 40 m/s).

Substituting the values, we get:

FL = 440 Hz * (343 m/s + 0 m/s) / (343 m/s + 40 m/s)

FL = 440 Hz * 343 m/s / 383 m/s

And, finally:

FL ≈ 393.7 Hz

So, just before your friend crashes into you (hopefully not too forcefully), you'll hear a slightly higher frequency of approximately 393.7 Hz. That's the sound of musical dedication combined with a touch of adrenaline!

Remember, music can be quite moving, especially when it's literally moving towards you at full speed. Stay safe and keep enjoying the harmonious running piccolo adventures!

To solve this problem, you can use the Doppler Effect formula for frequency shift:

f' = (v + vr) / (v + vs) * f

Where:
f' is the observed frequency
f is the source frequency
vr is the velocity of the observer (you)
vs is the velocity of the source (your friend)
v is the speed of sound in air (approximately 343 m/s)

In this case, your friend is running towards you with a velocity of 40 m/s, and the source frequency is 440 Hz. Therefore, you can plug in the values to find the observed frequency just before she runs into you:

f' = (343 + 0) / (343 + 40) * 440

Simplifying this expression:

f' = 343 / 383 * 440

Evaluating this expression:

f' ≈ 392.2 Hz

Therefore, just before your friend runs into you, you will hear a frequency of approximately 392.2 Hz.

To solve this problem, you can use the Doppler effect equation to calculate the frequency you hear just before your friend runs into you.

The Doppler effect equation for frequency is given by:

fL = fs ((v + vL) / (v + vs))

where:
- fL is the observed frequency (what you hear)
- fs is the source frequency (the frequency played on the piccolo)
- v is the speed of sound in air (which is approximately 343 m/s at room temperature)
- vL is the velocity of the listener (you) and
- vs is the velocity of the source (your friend).

In this case, your friend is running towards you, which means her velocity (vs) is positive, and your velocity (vL) is assumed to be zero since you mentioned you are waiting for her to run into you.

So, the equation simplifies to:

fL = fs (v / (v + vs))

Now let's plug in the given values:
- fs = 440 Hz (the frequency played on the piccolo)
- vs = 40 m/s (the velocity of your friend)
- v = 343 m/s (the speed of sound in air)

Substituting these values into the equation, we get:

fL = 440 ((343) / (343 + 40))

Now we can calculate the observed frequency (fL):

fL = 440 (343 / 383)

fL ≈ 391.86 Hz

Therefore, just before your friend runs into you, you would hear an approximate frequency of 391.86 Hz.