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The Big Wave Question

First, we discuss about what is wave. A wave is a disturbance, which travels in the medium. In a wave motion there is only the transference of energy and momentum from one point to another without any actual transportation of matter between these points. 

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Now let us discuss some big wave question.Image on wavesImage on wavesSome questions based on wavesLet us discuss some wave question.Example1:What are the amplitude, wavelength and velocity of the wave represented by?`phi(x,t) = 5 sin (6pit - 4x)`Where, x is the distance and t be the time, and they all are in the SI units?Solution:The given equation is:`phi(x, t) = 5 sin (6pi t -4x) = 5 sin 2 pi (3t -(4x )/ (2pi))`Compare it with the standard equation`phi(x,t) = r sin 2pi (t/T -x/(lambda))`We get, r = 5m that means the amplitude is 5 metre.1/T = 3 or f = 3 Hz1/λ= 4 / 2Π or λ = Π/2 that means the wavelength is Π/2 metre. 

 As velocity v = fλv = 3 × Π/2 = 4.71 metre per second.Example2:A wave travelling along a string is described by`y (x,t) = 0.005 sin (80.0 x -3.0 t)`In which the numerical constants are in SI units. Calculate (a) amplitude, (b) wavelength and (c) the period and frequency of the wave. Also, calculate the displacement y of the wave at a time 20 seconds and at a distance 30.0 cm.Solution:The given equation is:`y (x,t) = 0.005 sin (80.0 x - 3.0 t)` 

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 Compare it with the standard equation`y (x,t) = r sin ((2pi x)/(lambda) - 2pi/T)`R = 0.005 metre = 5 mm that means amplitude = 5 mmCoefficient of x = 2Π / λ = 80λ = 2Π / 80 metre = 7.85 cmCoefficient of t = 2Π / T = 3T = 2Π/ 3 = 2.09 secondFrequency f = 1/T = 1/ 2.09 = 0.48 HzDisplacement of wave at x = 30 cm and t = 20 second isy = 0.005 Sin (80 × 0.3 – 3 × 20) = 0.005 Sin (-36 radians) = 0.Conclusion for the questions based on wavesFrom the discussion made above, we can conclude that the questions related to wave can be determined by using suitable equations and can be useful in solving big questions.