A body completes 50 oscillations in \(20 \mathrm{~s}\). What is the frequency?

Oscillations are a fundamental concept in physics, describing the repetitive motion of an object around a central point or equilibrium position. This movement can be seen in a variety of systems, from the back-and-forth swing of a pendulum to the vibrations of an atom in a solid.
Oscillations occur when a system is displaced from its equilibrium position and experiences a restoring force that is proportional to the displacement, following Hooke's Law. Depending on the system, these oscillations can be mechanical, like a spring, or electromagnetic, such as the alternating current in electrical circuits.
Understanding oscillation is critical for various applications in physics and engineering, including the design of buildings and bridges, the functioning of clocks and watches, and the transmission of radio waves.

Frequency is an essential characteristic of oscillations, representing how often a repeating event occurs per unit time. It is determined by counting the number of complete cycles or oscillations that occur within a specific time frame.
To calculate frequency, the following formula is used:
\[\begin{equation} Frequency = \frac{Number\;of\;oscillations}{Time\;taken} \end{equation}\]
Interpreting the given problem, we observed a body completing 50 oscillations in 20 seconds. Applying this formula, we divide the total number of oscillations by the time duration to find the frequency. It's essential to ensure the time unit is in seconds to conform to the standard units for frequency. Calculating frequency correctly is crucial in various scientific and technological realms, such as acoustics, electronics, and communication systems.

The Hertz, symbolized as Hz, is the unit of frequency in the International System of Units (SI). It is defined as one oscillation or cycle per second.
When an object oscillates 50 times in 20 seconds, it has a frequency of 2.5 Hz, meaning it completes 2.5 cycles each second. The term 'Hertz' commemorates Heinrich Hertz, a pioneering physicist who made significant contributions to the understanding of electromagnetic waves.
The concept of Hertz is vital across many scientific disciplines. For instance, in acoustics, the pitch of a sound is determined by its frequency measured in Hertz. In electronics, the clock speed of a processor is indicated in gigahertz (GHz), or billions of cycles per second. Understanding and correctly utilizing the unit of Hertz allows for accurate measurement and communication of the rate of oscillations or cycles, which is central to physics and engineering.