We know that the number of complete vibrations of a vibrating particle in one second is called its frequency. Frequency is denoted by f. Again the time period is the time of one complete vibration.
If the time period is T, than in T second, the number of vibration is 1
Therefore, the number of vibration in one second is = 1/T
The number of vibration in 1 second is frequency. So, the frequency, f = 1/T
Mathematical example: The wavelength of sound produced by an object in the air is 20 cm .If the velocity of sound in the air is 340 ms-1, find the frequency and period of the object.
Here, Wave-length, γ = 20 cm = 0.2 m
Sound-velocity = 340 ms-1
Frequency, f =?
Period (time), T = ?
We know, Velocity = fγ
So, f = v/γ = 340 ms-1 / 0.20 m = 1700 Hz
And T = 1/f = 1 / 1700 s-1 = 0.000588 s = 5.88 x 10-4 s
The frequency 1700 Hz; Period (time) 5.88 x 10-4 s