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. [Pg.147]

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, [Pg.148]

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 [Pg.148]

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. [Pg.148]

The ratio to / u is usually defined by letter k, referred to as the wavenumber [Pg.149]

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