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?

Verified step by step guidance

1. Identify the fundamental frequencies for notes A and E, which are 440 Hz and 659 Hz respectively.
2. Calculate the third harmonic of the A note by multiplying the fundamental frequency of A (440 Hz) by 3. This gives the frequency of the third harmonic of A.
3. Calculate the second harmonic of the E note by multiplying the fundamental frequency of E (659 Hz) by 2. This gives the frequency of the second harmonic of E.
4. Find the frequency difference between the third harmonic of the A note and the second harmonic of the E note by subtracting the frequency of the second harmonic of E from the frequency of the third harmonic of A.
5. The result from the previous step gives the frequency difference between the third harmonic of the A note and the second harmonic of the E note.