Final answer:
Tension is the same throughout a massless and ideal (frictionless) string because the system is in static equilibrium, where forces must balance out. For strings at equal angles, the components of the tension force are the same, which satisfies the conditions for equilibrium.
Step-by-step explanation:
When considering why tension in a string is the same even if the weights of the masses are different, we can look at the properties of waves on a string and the conditions for static equilibrium. The velocity of a wave on a string depends on the tension and the linear mass density. According to physics principles, the tension is equal to the weight of the hanging mass (Tension = Mass x Gravity). Since a string can be considered massless and friction in an ideal pulley is negligible, the tension remains constant throughout the string.
In the context of static equilibrium, all the forces acting on the mass must balance out. This means that for strings in equilibrium, the tension at one end of the string must balance the tension at the other end, as the forces must be equal and opposite to maintain equilibrium. Moreover, if the system involves multiple strings at different angles, the tension components in each direction must sum to zero. The tension could differ if the angles of the strings concerning the horizontal are different; however, if the strings are oriented identically, then the components of the tension force in any given direction will be the same.
For example, a system with a mass suspended by two strings connected at a knot and hanging at equal angles will have the same tension in both strings, as the force of gravity is evenly distributed between them. This satisfies the equilibrium conditions.