The Period of a Wave is defined as time required in completing a wave cycle.A wave travels in a pattern similar to sine curve as shown below:A wave cycle is the said to be completed when a particle on this curve starts its motion at any point and reaches to the same position in phase to its starting position while moving in forward direction.
For example if we consider the particle to start at mean position then it will reach to the mean position firstly by going through crest. But at this point it is not in the phase with the starting position. ‘In phase’ means that if at the starting point particle was moving towards crest then at the other point also it should move towards the crest. But it is not true for this case.Now the particle will reach the mean position again for the second time after travelling through trough. At this mean position it is in the phase with initial position.
This cycle is known as wave cycle and the time required for covering this cycle is called time period of the wave. So one can calculate period by the time required between two consecutive crests or troughs.Period is denoted by the letter T. Period of a Wave Formula is given as:T = 1/fHere f is frequency of the wave and T is period.We know that a wave equation is given by the relation:V = f λHere V and λ is velocity and wavelength while f is its frequency.f = v/λHence Period of a Wave Equation can be given as:T = λ/v (as T = 1/f and f = v/λ)So period or time period = wavelength /velocityIts unit is that of time which is second (s), milli second etc.Finding the Period of a Wave requires finding its frequency.
For a sine wave, which is denoted by the equation y = A sin (ωt + φ), linear frequency is ω / (2π). Here ω is angular frequency and is given in radians.Hence period is T = 1/f = 1/(ω/2π) = (2π) / ωT =Problem based on time period:Ques.) Calculate the period of wave whose wavelength is 0.04 m and speed is 200 m/s. also calculate its frequency.Sol.) Period = λ/v = 0.04/200 = 2 * 10-4 seconds.Also frequency = 1/time period= 1/ 2 * 10-4= 0.5 * 104 Hz.