# Answer to Question #21460 in Mechanics | Relativity for Gaurav

Question #21460

in case of a wave ,prove that v=1/T, where v is the frequency and T is time period of the pendulum.

Expert's answer

in case of a wave ,prove that f=1/T, where f is the frequency and T is time period of the pendulum.

Frequency is the number of occurrences of a repeating event per unit time. The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency. For periodic waves, frequency has an inverse relationship to the concept of wavelength; simply, frequency is inversely proportional to wavelength λ:

f = v/λ.

On the other hand, the phase velocity of a wave is the rate at which the phase of the wave propagates in space:

v = λ/T.

Therefore,

f = (λ/T)/λ = 1/T.

Frequency is the number of occurrences of a repeating event per unit time. The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency. For periodic waves, frequency has an inverse relationship to the concept of wavelength; simply, frequency is inversely proportional to wavelength λ:

f = v/λ.

On the other hand, the phase velocity of a wave is the rate at which the phase of the wave propagates in space:

v = λ/T.

Therefore,

f = (λ/T)/λ = 1/T.

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