Question

When plucked, the E string on a violin has a frequency of 659 cycles per second. What sine function represents this note when it is graphed with an amplitude of 2.5 units? Let x represent the number of seconds.

Answer 1

The general form of a sinusoidal function is: f(x) = a*sin (bx-c) + d, for b > 0, where,

a = |amplitude|
T (period) = 2π/b; T = 1/f(frequency)
phase shift = c/b
vertical shift = d

Thus, given the frequency, the period can be calculated, followed by the value for b. The amplitude is already given. It is assumed that there is no phase shift or vertical shift, thus, c = 0, d = 0. The sine function is then represented by: f(x) = 659*sin(4141x)