An equation of a plane traveling wave

For the majority of problems it is important to know the dependence of oscillations of different points of media at a given instant This dependence can be considered as determined if the amplitudes and phases of oscillation are known. For transverse waves it is also necessary to know the polarization. For a plane one-dimensional polarized wave it is sufficient to have an expression defining the displacement of any wave point of (x,i) with the coordinate X in the instant of time t. Such an expression is called an equation of wave. 

Find the expression x,f) for the displacement of particles that are at distance x from the wave s source (origin). The wavefront covered this distance in time t = jc/v. This means that the vibrations at point (plane) x will be behind by the time t from that in origin. These points will also accomphsh the harmonic oscillations but with propagation delay x. In the absence of damping the oscillation amphtude is constant. Therefore, 

Find the relationship of wavelength X with other values, characterizing the wave propagation in a definite media. In accordance with the definition of the wavelength we can write 

This expression allows another definition of the wavelength wavelength is the distance a wave can propagate for a time equal to the period of oscillation. 

The ratio to / u is usually defined by letter k, referred to as the wavenumber 

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