Question

What is the S.I. unit of the frequency?

Answer 1

Hint: Convert the mathematical formula of frequency i.e., \[f=\dfrac{1}{T}\]into basic units in the MKS system and by doing so you will be capable of giving required units.

Complete step by step answer:

When we pluck a guitar string, the resulting sound has a steady tone and lasts a long time. Each successive vibration of the string takes the same time as the previous one. We define periodic motion to be a motion that repeats itself at regular time intervals, such as exhibited by the guitar string or by an object on a spring moving up and down.
Now, the time to complete one oscillation remains constant and is called the period T. Its units are usually seconds, but may be any convenient unit of time. The word period refers to the time for some event whether repetitive or not; but we shall be primarily interested in periodic motion, which is by definition repetitive.

A concept closely related to period is the frequency of an event. For example, if you pay any bill twice a month, the frequency of payment is two per month and the period between one payment to another payment is half a month.

Frequency f is defined to be the number of events per unit time. For periodic motion, frequency is the number of oscillations per unit time. The relationship between frequency and period is,

\[f=\dfrac{1}{T}\]

On writing the basic units in MKS system we get,

\[\text{1hertz=}\dfrac{\text{1cycle}}{\text{1second}}\]

The SI unit for frequency is cycle per second, which is named as Hertz (Hz).

Additional Information:
The term Hertz (Hz) has been kept in honour of German physicist Heinrich Hertz. Generally, when we say one hertz it means that an event reoccurs again and again with repetition as once per second.

Note: Students usually try to memorize the SI units, but it is a wrong way to do this type of question. Students should only memorize the basic formulas, and they should convert the given formula into basic units to dimensional formula or SI units.