Beat frequencies/tension force of violin strings while tuning--please help 1. The problem statement, all variables and given/known data To tune your violin, you first tune the A string to the correct pitch of 440 Hz, and then you bow both it and the adjoining string simultaneously, all the while listening for beats. While bowing the A and E strings, you hear a beat frequency of 3.00 Hz and note that the beat frequency increases as the tension on the E string is increased. (The E string is to be tuned to 660 Hz) (a) Why are the beats produced? 2. Relevant equations 3. The attempt at a solution I wrote that the beats were caused due to constructive/destructive interference, but the answer is that "The fundamentals of A and E differ too much to cause a beat frequency of 3hz, therefore it must be caused by the harmonics of A and E." It then says " So the E string must be slightly greater then 660hz because the beat frequency increases as the tension force increases." I understand that the beat frequency increases as the tension force increases, maybe not why, but ok, I hear it, but I don't get how he figured out the E string must be slightly greater then 660hz.. How can you tell the beat freq increased at all? I don't really get how he came to that conclusion. What if it was lower then 660hz? What would the beat freq look like? Also, what really is a fundamental or harmonic? I know what it means in terms of calculating stuff, but what is it? Is is different sections of the wave? Is it cycles of the wave? For every wave is there a fundamental wave, a harmonic wave (1,2,3,4 and so on)? I just dont get what they are in essence I guess.