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I am confused over this one...my textbook says that wave speed is the speed with which the wavefront travels which, to me, seems like they are the same thing but their definition looks different, to me.

Wavefront: A wavefront is a surface where all of the particles are vibrating in the same phase.

Wave: The disturbance which transfers energy through matter in space.

Does this mean that wavelets in wavefronts are the matter which transfer energy in space and hence cause wave disturbances according to these definitions? Can somebody help me with how should I relate these two definitions.

P.S-All definitions are from my school textbook.

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A wavefront is a surface where some particular condition holds. It is a locus of points.

The wave is the whole phenomenon of a propagating oscillation.

In theory the wave extends through all space in three dimensions. A wavefront is only a surface through the wave (typically a surface that is perpendicular to the direction the energy is travelling). You could define an infinite number of wavefronts associated with any particular wave.

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The textbook is giving you a clumsy definition of what physicists call phase velocity vs group velocity.

Phase velocity: This is the velocity of the disturbance, e.g. the velocity of a crest of the wave. In your case this is the "wave speed", because it is the velocity of the wavefront.

Group velocity: This is the velocity of the particules of matter. This velocity transports matter, it is the speed of the energy transfer.

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