**Unformatted text preview: **Problem 3: Consider an "A" string on a guitar, which is "fixed-fixed" on the guitar.
The length of the string that is free to vibrate is L=64.8 cm. The linear density of
the string is pi=3.5x10-2 g/cm.
A - What is the wave number (spatial frequency) k in radians/cm that corresponds
to the first harmonic?
B - What tension in newtons is required to tune the string to the desired
fundamental frequency (first harmonic) off=110 Hz?
C - The string is "plucked" by producing an initial displacement h=0.5cm at x=L/2
then releasing the string. Plot y(x, t) at t=0 from x=0 to x=L.
D - Using your knowledge about the problem and the simplest method possible,
determine the Fourier coefficient A1.
E - Using your knowledge about the problem and the simplest method possible,
determine the Fourier coefficient B1.
F - Using your knowledge about the problem and the simplest method possible,
determine the Fourier coefficient A2.
G - Using your knowledge about the problem and the simplest method possible,
determine the Fourier coefficient B2.
H - Plot the displacement of the first and second harmonics from x=0 to x=L at
t=0. Note: this is the first two terms of Kinsler equation (2.10.11) [Alsin(kix) and
Asin(kzx)]. (use MATLAB or origin)...

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- Fall '19
- 2 g, 0.5cm