Final answer:
The statement is true; waves do propagate faster in a less dense medium when the stiffness is constant, because the wave encounters less mass and resistance.
Step-by-step explanation:
The statement 'Waves propagate faster in a less dense medium if the stiffness is the same' is true. The speed of wave propagation is determined by the properties of the medium through which the wave is traveling. According to the formula for the speed of a wave (v), where v = √(stiffness/density), if the stiffness (or modulus of elasticity) of the medium remains constant, and the density decreases, the wave speed will indeed increase.
This is because the wave has less mass to move through in a less dense medium, allowing it to propagate quicker. We can observe this in different materials; for example, sound waves travel faster through air (less dense) than through water (denser), while maintaining the same stiffness.