• Support PF! Buy your school textbooks, materials and every day products Here!

Waves/Hooke's Law Problem

  • #1
372
0
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:

------------------------------------------------------------------------------------------------------------------
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 Δl.

(a) What is the speed (in terms of m, Δl, 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

------------------------------------------------------------------------------------------------------------------
Comments:

(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

This gives: t = [2&radic;(&Delta;l)]/&radic;(k;m)

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

This gives: t = [1/&radic;(k;m)]

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

Thanks a lot!
 

Answers and Replies

  • #2
372
0
Just a correction

Over comment for (b) [squ](k;m) = [squ](k/m)
 

Related Threads on Waves/Hooke's Law Problem

Replies
12
Views
1K
  • Last Post
Replies
7
Views
5K
  • Last Post
Replies
4
Views
523
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
2
Views
22K
  • Last Post
Replies
3
Views
4K
  • Last Post
Replies
10
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
2K
Top