The physics
Two pulses on one string pass through each other. Where they overlap, their heights add with their signs.
y = y₁ + y₂
Two waves of the same frequency add to one wave. Its amplitude depends on their phase gap δ.
A² = A₁² + A₂² + 2A₁A₂ cos δ δ = 360° × Δx / λ
A pulse that hits a tied end comes back upside down. A ring on a smooth pole is a free end. It sends the pulse back upright.
Two strings can meet at a joint. There, part of the pulse bounces back and part goes on. With one tension, the speed goes as 1/√μ.
r = (v₂ − v₁)/(v₁ + v₂) t = 2v₂/(v₁ + v₂) = 1 + r