Question

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

Answer 1

`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`