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Progressive Wave A progressive wave is defined as one in which the wave profile moves forward with the wave's speed. Both transverse and longitudinal waves are progressive waves. In a progressive wave, the amplitude and frequency of particle vibrations are the same, but the phase of the vibration varies from point to point along the wave. Progressive Wave Equation Suppose that the wave moves from left to right with a displacement velocity of v in which each article vibrates with a simple harmonic motion. However, when compared to the motion of the particle o at the origin O (at x = 0), subsequent particles to the right have phase lag. The vibrating particle's displacement y at origin O is given by, y = a sin  ω t      ........ (1) where 'a' is amplitude, 't' is time: ω  = 2πf, is the angular velocity, where f is the frequency of vibration. Consider a particle P at distance x from the origin as in fig. Φ be the phase lag of the particle P and λ be the wavelength....