Sound If a string with a fundamental frequency of
110
hertz is plucked in the middle, it will vibrate at the odd harmonics of
110
,
330
,
550
,
…
hertz but not at the even harmonics of
220
,
440
,
660
,
…
hertz. The resulting
P
pressure on the ear-drum caused by the string can be approximated using the equation
P
t
=
0.003
sin
220
π
t
+
0.003
3
sin
660
π
t
+
0.003
5
sin
1100
π
t
+
0.003
7
sin
1540
π
t
,
where
P
is in pounds per square foot at a time of
t
seconds after the string is plucked. Source: Fundamentals of Musical Acoustics and The Physics and Psychophysics of Music: An Introduction.
a. Graph
P
t
on
0
,
0.01
.
b. Find
P
'
0.002
and interpret.