Mathematics & Music
(AMath390)
K.A. Morris
Dept. of Applied Mathematics, University of Waterloo
c 2016
1
Introduction
What is Music?
From a Google search.
vocal or instrumental sounds (or both) combined in such a way as to
produce beauty of form, harmony

AMath390
Math & Music
Assignment # 3
Fall 2014
Due: noon Oct. 6 in dropbox 6 slot 3 (s.1 ) or slot 4 (s. 2)
1. p
The length of many flutes is 66cm and the diameter is 2cm. The speed of sound in air c =
P 0 (0 ) depends strongly on temperature and slightly

AMath390
Math & Music
Assignment #1 Due:
Fall 2016
noon Sept. 22 in dropbox 6 slot 3 (s.1 ) or slot 4 (s. 2)
1. Consider the dierential equation
y(t) + ! 2 y(t) = 0.
(1)
(a) Show that for any constants c, ,
y(t) = c sin(!t + )
(2)
is a solution to the die

Mathematics & Music
(AMath390)
K.A. Morris
Dept. of Applied Mathematics, University of Waterloo
c 2016
1
Introduction
What is Music?
From a Google search.
vocal or instrumental sounds (or both) combined in such a way as to
produce beauty of form, harmony

Mathematics & Music
(AMath390)
K.A. Morris
Dept. of Applied Mathematics, University of Waterloo
c 2016
1
Introduction
What is Music?
From a Google search.
vocal or instrumental sounds (or both) combined in such a way as to
produce beauty of form, harmony

Mathematics & Music
(AMath390)
K.A. Morris
Dept. of Applied Mathematics, University of Waterloo
c 2016
1
Introduction
What is Music?
From a Google search.
vocal or instrumental sounds (or both) combined in such a way as to
produce beauty of form, harmony

AMath390
Math & Music
Fall 2014
Assignment # 4
SOLUTIONS
1. Consider a drum consisting of a membrane stretched over a square frame, of length ` on
each side. Let the tension be T (N/m) and the density (kg/m2) .
(a) Write down the partial differential equa

AMath390
Math & Music
Assignment # 4
(s. 2)
Fall 2014
Due: noon Friday Oct. 21 in dropbox 6 slot 3 (s.1 ) or slot 4
1. Consider a drum consisting of a membrane stretched over a square frame, of length ` on
each side. Let the tension be T (N/m) and the den

Mathematics & Music
(AMath390)
K.A. Morris
Dept. of Applied Mathematics, University of Waterloo
c 2016
1
Introduction
What is Music?
From a Google search.
vocal or instrumental sounds (or both) combined in such a way as to
produce beauty of form, harmony

Mathematics & Music
(AMath390)
K.A. Morris
Dept. of Applied Mathematics, University of Waterloo
c 2016
1
Introduction
What is Music?
From a Google search.
vocal or instrumental sounds (or both) combined in such a way as to
produce beauty of form, harmony

AMath390
Math & Music
Assignment # 2
Fall 2014
Due: noon Sept. 29 in dropbox 6 slot 3 (s.1 ) or slot 4 (s. 2)
1. Draw graphs of the functions
sin(220t) +
1
sin(440t)
2
and
1
cos(440t)
2
Explain why these sound the same, even though the graphs look quite d

AMath390
Math & Music
Assignment # 5 Due:
Fall 2016
noon Nov. 3 in dropbox 6 slot 3 (s.1 ) or slot 4 (s. 2)
1. (a) Find the period T , and coefficients in the complex Fourier series for
f (t) = 6 + 4 cos(t)
3 sin(4t).
(Hint: You do not need to compute any