Frequency:

The frequency, is represented by f, of a wave is the opposite of the period. That is, f = 1/T, and T = 1/f. In olden days, frequency was identified in cycles per second, abbreviated as cps. High frequencies were expressed in megacycles, kilocycles, or gigacycles, symbolizing thousands, millions, or billions of cycles per second. These days, the standard unit of frequency is termed as the hertz, abbreviated as Hz. Therefore 1 Hz = 1 cps, 10 Hz = 10 cps, and so forth.

Higher frequencies are given in kilohertz (kHz), megahertz (MHz), gigahertz (GHz), and terahertz (THz). The relations are as follows:

1 kHz = 1,000 Hz = 10³ Hz

1 MHz = 1,000 kHz = 10⁶ Hz

1 GHz = 1,000 MHz = 10⁹ Hz

1 THz = 1,000 GHz = 10¹² Hz

PROBLEM:

The period of an ac wave is 5.000 x 10^-6 s. Compute the frequency in hertz? In kilohertz? In megahertz?

SOLUTION:

At first, find the frequency f_Hz in hertz by taking the reciprocal of the period in seconds:

f_Hz = 1/(5.000 x 10^-6) = 2.000 x 10⁵ Hz

Next, divide f_Hz by 1,000 or 10³ to obtain the frequency f_kHz in kilohertz:

f_kHz = f_Hz/10³= 2.000 x 10⁵/10³ = 200.0 kHz

Finally, divide f_kHz by 1,000 or 10³ to obtain the frequency f_MHz in megahertz:

f_MHz = f_kHz/10³ = 200.0/10³ = 0.2000 MHz