Math 592 (The Math of Music)
Quiz 4
Spring 2015
Drew Armstrong
1. In the one-dimensional wave equation utt = c2 uxx , what does the number c represent? How
can you compute c in the case of a stretched
Math 592 (The Math of Music)
Quiz 3
Spring 2015
Drew Armstrong
1. Write down the solution of the undamped harmonic oscillator x (t) + 2 x(t) = 0 with
initial conditions x(0) and x (0).
x(t) = x(0) cos
Math 592 (The Math of Music)
Quiz 1
Spring 2015
Drew Armstrong
1. Suppose a certain kind of guitar string has a linear density of 0.02 kg/m. If you tighten
the string to a tension of 800 kg m/s2 , wha
Math 592
Homework 2
Spring 2015
Drew Armstrong
1. Beats Again. Show that the phenomenon of beats is independent of phase shifts. [Hint:
Consider the superposition sin(f1 2t + ) + sin(f2 2t + ).]
Apply
Math 592 (The Math of Music)
Quiz 2
Spring 2015
Drew Armstrong
1. Write down Eulers Formula.
eit = cos t + i sin t
OR
exp
0 t
t 0
=
cos t sin t
.
sin t cos t
2. Write down the trigonometric identity t
Math 592
Homework 3
Spring 2015
Drew Armstrong
A Justly Tuned Chromatic Scale.
On this homework you will compute the best rational approximations to the notes of the equaltempered chromatic scale. The
Math 592
Homework 1
Spring 2015
Drew Armstrong
0. Compute the length of a chord of the unit circle subtended by an arc of length t.
Consider the chord and the half-chord subtended by an arc of length