Soln MAE 518 Acoustic Radiation 1 Homework #2 Do the following

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Soln MAE 518
Acoustic Radiation 1
Homework #2
Do the following problems from the text book,
Problem 2.8.1
y  4cos  3t  2 x  propagating on a string of linear density 0.1g/cm
x are in centimeters and t is in seconds.
Consider the wave form
where y and
(a) What are the amplitude, phase speed, frequency, wavelength, and wave number?
(b) What is the particle speed of the element at x  0, t=0 ?
Problem 2.10.1
A stretched string of length L is plucked at a position L/3 by producing an initial
displacement h and then releasing the string.
Determine the resulting amplitudes for the fundamental and first three harmonic
overtones.
Sketch the wave shapes of these individual waves and the resulting shape of the string at
t =0 and t = L/c where c is the transverse wave speed on the string.
Correction: in the solution of An, there should be no “cos” term
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