Flute player initial frequency?

[Wimpalot]

Homework Statement

A flute player hears four beats per second when she compares her note to a 587 Hz tuning fork (the note D). She can match the frequency of the tuning fork by pulling out the "tuning joint" to lengthen her flute slightly. What was her initial frequency?

Homework Equations

Not sure if it actually is relevant but:
f_beat = |f₁ - f₂|

The Attempt at a Solution

I have no idea what to do for this one. I'm not even entirely sure what is going on

 

[TomHart]

Have you ever tuned an instrument? I will assume that you have not. If you have two instruments (whatever they are - flutes, guitars, digitally generated sine waves, etc.), and you strike a sound on each of them, if the frequencies of those two sounds are slightly different, you will be able to hear that frequency difference. The effect you will hear is a modulating amplitude. In other words, you will hear the combined sound getting louder and softer at a certain frequency. That frequency is called the beat frequency.

One thing you could do to observe this effect visually is create an Excel sheet. Generate two sine waves - one at, say, 440 Hz (note A4) and another at, say, 444 Hz. Then mathematically add those 2 waveforms and plot the result. You will be able to see the 4 Hz beat frequency.

One other important part of this problem that may not be obvious to everyone is this: When the length of the flute is increased, the pitch (frequency) of the sound decreases.

Edit: Here is a short video clip to demonstrate beat frequency.

 

[Wimpalot]

Have you ever tuned an instrument? I will assume that you have not. If you have two instruments (whatever they are - flutes, guitars, digitally generated sine waves, etc.), and you strike a sound on each of them, if the frequencies of those two sounds are slightly different, you will be able to hear that frequency difference. The effect you will hear is a modulating amplitude. In other words, you will hear the combined sound getting louder and softer at a certain frequency. That frequency is called the beat frequency.

One thing you could do to observe this effect visually is create an Excel sheet. Generate two sine waves - one at, say, 440 Hz (note A4) and another at, say, 444 Hz. Then mathematically add those 2 waveforms and plot the result. You will be able to see the 4 Hz beat frequency.

One other important part of this problem that may not be obvious to everyone is this: When the length of the flute is increased, the pitch (frequency) of the sound decreases.

Edit: Here is a short video clip to demonstrate beat frequency.

Thanks, that helps me understand what it is but I still have no idea how to do the question

 

[TomHart]

fbeat = |f1 - f2|

Your equation is appropriate. If you know f_beat (which you do), and you know f₁ (which you do), there are only 2 possible solutions for f₂.

 

[Wimpalot]

Your equation is appropriate. If you know f_beat (which you do), and you know f₁ (which you do), there are only 2 possible solutions for f₂.

Right of course, thank you

 

[rude man]

Only 2 possible solutions ...

So have you figured out which one?

 

[Wimpalot]

So have you figured out which one?

I think it was 585Hz. Sorry it has been a while since I did this problem. Honestly I think I just guessed at whether it was 585 or 589

 

[rude man]

I think it was 585Hz. Sorry it has been a while since I did this problem. Honestly I think I just guessed at whether it was 585 or 589

Your choices are 587+4 = 591 and 587 - 4 = 583.

Re-consider the problem statement: "She can match the frequency of the tuning fork by pulling out the "tuning joint" to lengthen her flute slightly." (Emphasis mine).