I have a decent background in physics, but something that has always confused me is how to think about how the tension of the string in a tennis racquet affects how the ball leaves the strings. For example, the traditional lore in tennis is that tauter strings will give more control, whereas looser strings will give the player more power (strings are more 'springy'). However, I struggle to find a clear explanation for this common statement. For example, if I think about conservation of momentum, I have a tennis racquet with a certain mass that is moving (sure, rotating to be accurate) and it contacts the tennis ball. One part of me thinks that the tension of the strings should have absolutely no effect on the speed of the ball after you hit it b/c since momentum is conserved, if you hit the ball with the same racquet speed, then the same momentum will be transferred. However, I also feel like this may not be true. Can someone talk with me about this? Is it the case that at a certain string tension, the ball hits the strings in a more harmonic manner so the ball isn't dampened as much?