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Though slinky coil is commonly used to demonstrate transverse and longitudinal waves, you must not quote it as an example for either of the waves.
Transverse waves are waves in which the direction of the wave is perpendicular to the direction of the vibration of the particles. Examples are light wave, water wave or all the waves in the electromagnetic spectrum (which light is one of the waves.
Longitudinal waves are waves in which the direction of the wave is parallel to the direction of the vibration of the particles. Example is sound wave (inludes ultrasound and infrasound)
Transverse Waves (slinky coil)
Longitudinal Waves (slinky coil)
Transverse Waves Animation
Longitudinal Waves Animation