The type of rubber band used inside some baseballs and golf balls obeys Hooke's law over a wide range of elongation of the band. A segment of this material has an un-stretched length (and a mass m. When a force F is applied, the band stretches an additional length Δℓ.

(a) What is the speed (in terms of m, Δℓ, and the spring constant k) of transverse waves on this stretched rubber band?

(b) Using your answer to (a), show that the time required for a transverse pulse to travel the length of the rubber band is proportional to l/√Δℓ if Δℓ << ℓ and is constant if Δℓ >> ℓ?