Question

How do you calculate the frequency of oscillation?

Answer 1

Frequency of oscillation:

1. It is the number of oscillations in the one-time unit, says in a second.
2. A pendulum that takes 0.5 seconds to make one full oscillation has a frequency of 1 oscillation per 0.5 seconds or 2 oscillations per second.

The formula for the frequency of oscillation:

1. The period (T) of the oscillation is defined as the time taken by the particle to complete one oscillation. After time T, the particle passes through the same position in the same direction.
2. The frequency of oscillation is simply the number of oscillations performed by the particle in one second.
3. In T seconds, the particle completes one oscillation.

$\therefore$, the number of oscillations in one second, i.e. its frequency f, is:

$\therefore \mathrm{f}=\frac{1}{\mathrm{T}}$

The oscillations frequency is measured in cycles per second or Hertz.

Example:

Calculate the frequency, in Hertz, for 120 oscillations in 2.0 seconds.

1. The frequency (f) of a wave is the number of full waveforms generated per second.
2. This is the same as the number of repetitions per second or the number of oscillations per second.
3. Time period(T) is the number of seconds per waveform or the number of seconds per oscillation.
4. It is clear that frequency and period are reciprocals. In the first case, there are 120 oscillations in 2.0 seconds.

$\therefore$ the frequency is given as,

$\begin{array}{rcl}\therefore \mathrm{f}& =& \frac{120}{2}\\ & \Rightarrow & \mathrm{f}=60\mathrm{hertz}\end{array}$