Answer Happy

1.) The steel strings on your Yamaha F335 (acoustic guitar) have a mass density of 2 g/m. You need to tune your lowest string to a D, (a fundamental frequency of 73.42 Hz) to play "Dear Prudence" by The Beatles. a) (4 points) If the string has a mass of 1.3 grams, what is the length of this string? b) (8 points) If this string was originally tuned to E, (fundamental frequency of 82.41 Hz), how much does the tension of the string need to be decreased to achieve the desired tuning of D_? c) (8 points) How far from the nut of the guitar (the end closest to the tuning pegs) should the 7th fret be placed to play the note A, for the dropped D tuning? Note that this interval represents a perfect fifth, which has a frequency 3/2 times the fundamental. How far from the nut should the 19th fret for A, (an octave above Ay, i.e. double the frequency of A,) be? d) (5 points) If you decide to pluck the string directly in the center, explain which of the Fourier Series Coefficients (A, and B.) will be excited. Will any modes be canceled? (You do not need to solve for specific coefficients in this question)