Piano tuners tune pianos by listening to the beats between the harmonics of two different strings. When properly tuned, the note A should have a frequency of 440 Hz and the note E should be at 659 Hz. a.What is the frequency difference between the third harmonic of the A and the second harmonic of the E?

Video transcript

Hey, everyone. So this problem is working with harmonics. Let's see what it's asking us. A guitarist is tuning his guitar using harmonics. When in tune the six string, the low E string should be at a frequency of 82. Hertz. And the fourth string, the D string should be at a frequency of 146.83 Hertz determine the frequency difference between the fourth harmonic of the sixth string and the third harmonic of the fourth string. Our multiple choice answers here are a 130. Hertz B 120.61 Hertz C 100.52 Hertz or D 110.85 Hertz. OK. So this is a straightforward problem about the frequency of, of harmonics. As long as we can recall that the frequency of the NTH node is given by the equation and multiplied by F one for that initial frequency. So we are given F E and F one for the D string. And so now we need to find the frequency of the fourth E string and that's going to equal four. That's the fourth node or the fourth harmonic multiplied by 0.41 Hertz. So that equals 329.64 Hertz. We're gonna do the same thing with the third harmonic of the fourth string or the D string that's going to equal three, multiplied by 146. Hertz. And that comes out to 440. Hertz. And now all we have to do is find the difference. So we subtract them. So the frequency of the third harmonic of the D string minus the frequency of the fourth harmonic of the E string is equal to 110 0.85 Hertz. And that aligns with answer choice D so D is the correct answer for this problem. That's all we have for this one. We'll see you in the next video.