Question

Which of the following represents the correct relationship between frequency and angular frequency?

• A. \( \omega = 2\pi f \)
• B. \( \omega = \pi f \)
• C. \( f = 2\pi \omega \)
• D. \( f = \pi \omega \)

Hint:

Frequency vs Angular Frequency. \(\omega = 2\pi f\). Where \(f\) is frequency in Hz (cycles/sec) and \(\omega\) is angular frequency in rad/sec. \(T = 1/f = 2\pi/\omega\), where T is the period.

Answer 1

The Correct Option is A

Frequency (\(f\)) is the number of cycles or oscillations per unit time, typically measured in Hertz (Hz), where 1 Hz = 1 cycle per second
Angular frequency (\(\omega\)) represents the rate of change of phase angle, typically measured in radians per second (rad/s)
Since one complete cycle corresponds to an angle of \(2\pi\) radians, the relationship between angular frequency and frequency is: $$ \omega (\text{rad/s}) = 2\pi (\text{rad/cycle}) \times f (\text{cycle/s}) $$ $$ \omega = 2\pi f $$ This relationship is fundamental in describing oscillations and waves
Option (1) correctly represents this relationship