The amplitude of gravitational waves generated by an asymmetrically tumbling dumbbell depends on both its speed and mass.
Gravitational waves are produced by the acceleration of mass. The more massive an object is, the greater the gravitational waves it can produce. This means that the mass of the dumbbell will have an impact on the amplitude of the gravitational waves it emits.
Additionally, the speed at which the dumbbell is tumbling affects the amplitude of the gravitational waves. As the object accelerates, the amplitude of the gravitational waves increases. This is similar to how the amplitude of electromagnetic waves (such as light) increases with the acceleration of charged particles.
Therefore, both the mass and speed of the asymmetrically tumbling dumbbell play a role in determining the amplitude of the gravitational waves it radiates.