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Assume that the length of the section that vibrates in the strings of a guitar is...

Assume that the length of the section that vibrates in the strings of a guitar is 1 m, this is the distance from the bridge to the nut. The second string from the top, out of six, is conventionally tuned to A two octaves below concert A. This is written as A2, and the note has a frequency of 110 Hz. The A-Major scale starting at A2, with the respective frequencies in the Pythagorean Tuning is:
A2: 110.00 Hz.   
B2:123.75 Hz
C#1: 139.22 Hz
D1: 146.67 Hz
E1: 165.00 Hz
F#1:185.63 Hz
G#1: 208.83 Hz
A1: 220.00 Hz

(a) When the A-string plays the note A2 = 110 Hz, the frequency f of the first harmonic is also 110 Hz. What is the wavelength of the first harmonic? What is the speed of a traveling wave on the string? Explain why increasing the tension in the string increases the frequency of the note the string plays.
(b) What is the wavelength of the second harmonic of this string? What is the frequency of this wave?
(c) If you place your finger just to the right of the 12th fret, the effective length of the string becomes 0.5 m. What are the wavelength and frequency of the first harmonic? What musical note is the string playing? How do your values compare to the result in the previous part? Explain.
(d) If you place your finger just to the right of the 7th fret, the effective length of the string becomes 2/3 m. What are the wavelength and frequency of the first harmonic? What musical note is the string playing? Explain.

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