what is a wave?define longitudinal and transverse waves.

a wave is ​the  periodic disturbance of the particles of a substance which may be propagated without net movement of the particles, such as in the passage of undulating motion, heat, or sound

In a longitudinal wave the particle displacement is parallel to the direction of wave propagation. The animation at right shows a one-dimensional longitudinal plane wave propagating down a tube. The particles do not move down the tube with the wave; they simply oscillate back and forth about their individual equilibrium positions. Pick a single particle and watch its motion. The wave is seen as the motion of the compressed region (ie, it is a pressure wave), which moves from left to right.

In a transverse wave the particle displacement is perpendicular to the direction of wave propagation. The animation below shows a one-dimensional transverse plane wave propagating from left to right. The particles do not move along with the wave; they simply oscillate up and down about their individual equilibrium positions as the wave passes by. Pick a single particle and watch its motion.  
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A WAVE IS A DISTURBANCE THAT MOVES THROUGH A MEDIUM WHEN THE PARTICLES OF THE MEDIUM SET THE NEIGHBOURING PARTICLES INTO MOTION
LONGITUDINAL WAVES ARE WAVES IN WHICH THE INDIVIDUAL PARTICLES OF THE MEDIUM MOVE IN A DIRECTION PARALLEL YO THE DIRECTION OF PROPAGATION OF THE DISTURBANCE.
TRANSVERSE WAVE IS A WAVE IN WHICH THE PARTICLES DO NOT OSCILLATE ALONG THE LINE OF WAVE PROPAGATION BUT OSCILLATE UP AND DOWN ABOUT THEIR MEAN POSITION AS THE WAVE TRAVELS.
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HOPE THIS IS HELPFUL.
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