Frequency Formula

Frequency refers to the number of cycles in a particular unit of time. The reason why the sky is blue or anything contains color can be easily explained by it. Furthermore, it can also explain why the voice of some individuals is deep while for others it is not deep. Also, frequency plays a big influence on the notes of a piano or other musical instruments. Learn the frequency formula here.

What is Frequency

Frequency refers to the number of occurrences of a repeating event taking place per unit of time. Furthermore, the period refers to the duration of time of one cycle in an event that is repeating. Therefore, the period happens to be the reciprocal of the frequency.

This number of occurrences is certainly an essential property of a wave. The waves surround people every day. Furthermore, light happens to be an electromagnetic wave and the sound of the fan is a sound wave. A wave is certainly a vibration and carries energy with it. Most noteworthy, the number of waves passing by each second refers to the frequency of the wave. Moreover, its measurement takes place in Hertz (Hz).

Frequency Formula

The SI unit which is hertz was named after Heinrich Rudolf. Furthermore, 1 hz refers to one cycle per second.

Frequency = 1/period = number of cycles/time

f = 1/T = N/t
T = period, the time which is required for one cycle
N = a particular number of cycles
t = a particular amount of time

Formula Derivation

First of all, it’s clear that f = 1/T = N/t. The ‘f’ is inversely proportional to the time taken so as to complete one oscillation. Furthermore, the time period = T. Therefore, ‘T’ refers to the amount of time taken for completing of one cycle. Above all, frequency without a doubt means the number of cycles that are completed in unit time.

Therefore, if an individual takes y seconds to complete one cycle, then the individual would complete 1/y cycles in one second. Consequently, it means that the time period (t) happens to be one second.
Hence, f is 1/y s^(-1).

Solved Examples on Frequency Formula 

Q1. A long pendulum takes 4 seconds to complete one back-and-forth cycle. Find out the frequency of the pendulum’s motion?

Answer: The period ‘T’ of the pendulum is 4 seconds. Therefore, one can find frequency by the following formula:

f = 1/T
f = 1/4
f = 0.25 cycles.

Hence, the frequency of the pendulum is 0.25 cycles. The writing of the units cycles usually takes place as “Hertz”, and its symbol is Hz. Therefore, the frequency of this particular pendulum is 0.25 Hz.

Q2. The tachometer in a car carries out the measurement of the revolutions per minute of the tires A car is traveling at a constant speed, and the reading of the tachometer 2200 revolutions per minute. Find out the frequency of the tires spinning. Also, find out the period in seconds.

Answer: The number of cycles or revolution = 2200. This certainly is the number of cycles which occur in one minute.
Therefore, the frequency would be:

f = N/t
f = 2200 cycles/ 1 minute = 2200 cycles/ 60 seconds
f = 36.666 cycles

This can also be written as 36.666 hertz. Now, we have to find the period from this. To find the period, rearrangement of the equation or formula which relates to period and frequency must take place.

f = 1/T
T = 1/f
T = 1/36.666
T = 0.027s

Hence, the period of the tires spinning is 0.027 s.