How do you calculate the period and frequency?

The time period is the time taken by a complete cycle of the wave to pass a point, Frequency is the number of complete cycle of waves passing a point in unit time. Angular frequency is angular displacement of any element of the wave per unit time.

What is Time Period?

In sinusoidal wave motion, as shown above, the particles move about the mean equilibrium or mean position with the passage of time. The particles rise till they reach the highest point that is the crest and then continue to fall till they reach the lowest point that is the trough. The cycle repeats itself in a uniform pattern. The time period of oscillation of a wave is defined as the time taken by any element of the string to complete one such oscillation. For a sine wave represented by the equation: y (0, t) = -a sin(ωt) The time period formula is given as:

\(T=\frac{2\pi }{\omega }\)

What is Frequency?

We can define frequency of a sinusoidal wave as the number of complete oscillations made by any element of the wave per unit time. For a sinusoidal wave represented by the equation: y (0,t) = -a The formula of the frequency with the SI unit is given as:

\(f=\frac{1}{T}=\frac{\omega }{2\pi }\)

One Hertz is equal to one complete oscillation taking place per second.

Frequency is the revolutions per second or number of wave cycles. The Frequency is expressed in Hertz (Hz).

Formula

If one considers any wave in terms of wavelength and velocity, the Frequency Formula is articulated as

Frequency formula 1

f=ν / λ
Where,
the frequency of the wave is f,
the wave velocity or wave speed is V,
the wavelength of the wave is λ.

If the light wave is considered, then the frequency is articulated as

Frequency formula 2

f=c / λ

Where

c is the velocity of light.

Frequency in terms of angular frequency is articulated as

Frequency formula 3

f= ω / 2π
Where ω is the angular frequency.

Frequency formula 4

f=1 / T

Where T is time period

The formula for the frequency of a wave is used to find frequency (f), time period (T), wave speed (V) and wavelength (λ).

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