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Tension is a reaction force applied by a stretched string (rope or a similar object) on the objects which stretch it. The direction of the force of tension is parallel to the string, towards the string.
Tension exists also inside the string itself: if the string is made up of two parts, tension is the force which the two parts of the string apply on each other. The amount of tension in the string determines whether it will break, as well as its vibrational properties, which are used in musical instruments.