Wave Packet SolutionSince the traveling wave solution to the wave equation is valid for any values of the wave parameters, and since any superposition of solutions is also a solution, then one can construct a wave packet solution as a sum of traveling waves: It is common practice to use to represent the quantity 2π/λ by k, which is called the wave vector. For a continuous range of wave vectors k, the sum is replaced by an integral:

Index Wave concepts Reference Tipler Elementary Modern Physics, Appendix B  

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Wave Packet DetailsA wave packet solution to the wave equation, like a pulse on a string, must contain a range of frequencies. The shorter the pulse in time, the greater the range of frequency components required for the fast transient behavior. This requirement can be stated as a kind of uncertainty principle for classical waves: The actual numbers involved depend upon the definition of the pulse width, but creating short pulses inherently requires a large frequency bandwidth. This is similar in nature to the uncertainty principle in quantum mechanics.

Index Wave concepts  

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Wave Packets from Discrete WavesIf discrete traveling wave solutions to the wave equation are combined, they can be used to create a wave packet which begins to localize the wave. This property of classical waves in mirrored in the quantum mechanical uncertainty principle. 
Index Wave concepts  

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