equation of a progressive wave propagate in a string is y= 0.02 sin 4 pie (2x-1st) where x and y are in meter and t in sec . find the amplitude, frequency,wave length, velocity, time period
Question
equation of a progressive wave propagate in a string is y= 0.02 sin 4 pie (2x-1st) where x and y are in meter and t in sec . find the amplitude, frequency,wave length, velocity, time period
Solution
The equation of the wave is given as y = 0.02 sin 4π(2x - t). This is in the form of y = A sin(ωt - kx), which is the equation for a sinusoidal wave.
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Amplitude (A): The amplitude is the maximum displacement from the equilibrium position. In the given equation, the amplitude is 0.02 m.
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Angular Frequency (ω): The angular frequency is the rate at which the wave oscillates in time. It is given by 2π times the frequency (f). In the equation, ω = 4π, so the frequency f = ω / 2π = 4π / 2π = 2 Hz.
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Wave Number (k): The wave number is the spatial frequency of the wave, specified in terms of radians per unit distance. It is given by 2π divided by the wavelength (λ). In the equation, k = 2, so the wavelength λ = 2π / k = 2π / 2 = π m.
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Velocity (v): The velocity of a wave is given by the product of its frequency and wavelength. So, v = f * λ = 2 Hz * π m = 2π m/s.
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Time Period (T): The time period is the reciprocal of the frequency. So, T = 1 / f = 1 / 2 = 0.5 s.
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