# Waves/Hooke's Law Problem

Hi,

Could you please give a hand with this question from the book "Fundamentals of Physics/Halliday, Resnick, Walker" - 6th ed, page 395, #22P. Here it goes:

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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 ustretched length l and mass m. When a force F is applied, the band stretches an additional length &Delta;l.

(a) What is the speed (in terms of m, &Delta;l, and 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 1/&radic;(&Delta;l) if &Delta;l << l and constant if &Delta;l >> l

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(a) v = &radic;([tau]/[mu]), where [tau] = F = k&Delta;l and [mu] = m/(l+&Delta;l). This gives: v = &radic;{[k&Delta;l(l+&Delta;l)]/m} --- This should be right.

(b) I'm not sure what happens in either case... my guess is that when:

&Delta;l << l, we have: v = &radic;[(kl)/m].

v = dl/dt Then: [&int;(0,&Delta;l)] dt = [&int;(0,&Delta;l)] (1/v) dl

That doesn't seem to fit, but could be close.

&Delta;l >> l, we have: v = &radic;{[k(&Delta;l)^2]/m}.

v = dl/dt Then: [&int;(0,&Delta;l)] dt = [&int;(0,&Delta;l)] (1/v) dl

That doesn't seem to fit, but could be close as well.

Thanks a lot!