Tension in a string in which a wave is present Why is the tension in a string carrying a transverse wave uniform throughout the string
 A: Although the approximation is rarely made explicit, when we say the tension is uniform we mean that we think that by far the majority of the tension comes from the way we stretched the string between its mounting points, so that the additional tension from the wave is insignificantly small. If the string were pulled very far from its resting position this would clearly not be the case (just imagine doubling the length of a rubber band by pulling the middle upwards) but when the string wave problem is set up we consider only very small waves that don't increase the length of the string very much.
To see how the approximation breaks down in an experiment, try to set up a wave in a loosely mounted string by stretching it taught and letting it go. It won't follow the wave equation's predictions, because the wave equation would have come from considering only the force from the "mounting" tension - which in that case would be small compared to the other forces, like the additional tension from the initial stretching.
