Question

The frequency of a hum that is generated by an engine is 270hz. If t starts at zero, which of the following would best describe this frequency over time?
(Don’t pay attention to the answer chosen)

Answer 1

Answer:

sin ( 2π(270)*t )

Step-by-step explanation:

Solution:-

- The frequency of the hum is denoted as k = 270 Hz.

- The displacement of the hum is modeled by a sinusoidal function.

- The trigonometric modelling of frequency generating systems is given in the following general form:

                               sin ( w*t ) + c

- Where,

              A: The amplitude of displacement e

              w: The angular speed of the hum

              c : The initial condition of displacement.

- Here, we will assume A = 1 and c = 0. The hum starts from time t = 0 seconds.

- The angular speed is the unit of speed that denotes the number of cycles in radians are undergone by the frequency generator device/person in unti time t.

- The angular speed is given by the following relation:

                             w = 2πk

                             w = 2π(270).

- The general model of the hum would be:

                             sin ( 2π(270)*t )