What is the frequency of #f(t)= sin(4t) - cos(7t)#?

1 Answer
Apr 23, 2017

#f_0 = 1/(2pi)" Hz"#

Explanation:

Given: #f(t)= sin(4t) - cos(7t)# where t is seconds.

Use this reference for Fundamental Frequency

Let #f_0# be the fundamental frequency of the combined sinusoids, in Hz (or #"s"^-1#).

#omega_1 = 4" rad/s"#
#omega_2 = 7" rad/s"#

Using the fact that #omega = 2pif#

#f_1 = 4/(2pi) = 2/pi " Hz"# and #f_2 = 7/(2pi)" Hz"#

The fundamental frequency is the greatest common divisor of the two frequencies:

#f_0 = gcd(2/pi " Hz", 7/(2pi)" Hz")#

#f_0 = 1/(2pi)" Hz"#

Here is a graph:

graph{y = sin(4x) - cos(7x) [-10, 10, -5, 5]}

Please observe that it repeats every #2pi#