What beat frequencies are possible with tuning forks of frequencies 258, 263, and 267 Hz?

What beat frequencies are possible with tuning forks of frequencies 258, 263, and 267 Hz ?

Enter your answers in ascending order separated by commas.
f1,f2,f3 = 4,5,9 Hz

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Well, those tuning forks are certainly in a harmonic relationship... They could form their own little band! Let's see what kinds of beat frequencies they can produce.

To calculate the beat frequency, we subtract the frequency of one tuning fork from the frequency of another. So let's take a look:

(263 Hz - 258 Hz) = 5 Hz
(263 Hz - 267 Hz) = -4 Hz
(258 Hz - 267 Hz) = -9 Hz

So, the possible beat frequencies are 5 Hz, -4 Hz, and -9 Hz. Now that's some serious harmonic dissonance going on! Just make sure to tell your ears to brace themselves for these wild beat frequencies.

To determine the beat frequencies possible with these tuning forks, we need to calculate the differences between their frequencies and find the common factors.

First, let's calculate the frequency differences between the tuning forks:
- For the first two forks, the difference is 263 Hz - 258 Hz = 5 Hz.
- For the second and third forks, the difference is 267 Hz - 263 Hz = 4 Hz.
- Finally, for the first and third forks, the difference is 267 Hz - 258 Hz = 9 Hz.

Now, let's find the common factors of these differences, which correspond to the possible beat frequencies:
- The factors of 5 Hz are 1 and 5.
- The factors of 4 Hz are 1 and 2.
- The factors of 9 Hz are 1 and 9.

So, the possible beat frequencies are 1 Hz, 2 Hz, 5 Hz, and 9 Hz.

f1 = 263 -258 = 5Hz

f2 = 267 - 258 = 11 hz,
f3 = 267-263 = 4 Hz