We propose the use of smartphone-based slow-motion video analysis techniques as a valuable tool for investigating physics concepts ruling mechanical wave propagation. The simple experimental activities presented here, suitable for both high school and undergraduate students, allows one to measure, in a simple yet rigorous way, the speed of pulses along a spring and the period of transverse standing waves generated in the same spring. These experiments can be helpful in addressing several relevant concepts about the physics of mechanical waves and in overcoming some of the typical student misconceptions in this same field.