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 string?
The number c is the speed of propagation. In t
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(t) +
x (0)
sin(t)
2. What is the frequency of the damp
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 , what is the speed of a disturbance in the string?
800
= 40
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 + ).]
Applying the identity sin(u) + sin(v) = 2 sin
u+v
2
cos
uv
2
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 that explains the phenomenon of beats. [Hint:
sin(u) + s
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 tool you will use is called continued fractions. Any i
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 t:
If crd(t) is the length of the chord then 1 crd(t) i