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

Standing waves, find distance

  • Thread starter nil1996
  • Start date
  • #1
301
7

Homework Statement


A string of length 1.5m with its two ends clamped is vibrating in fundamental mode. Amplitude at the center of the string is 4mm. Find the distance between the points who have amplitude 2mm.


Homework Equations


y=Asinkxcoswt
λ=2*L

The Attempt at a Solution



First of all i was trying to get the distances of the points from one of the nodes.
so putting t=0 i get y=Asinkx

k=2π/λ
λ=2*L = 2*1.5 = 3

so y= Asin[itex]\frac{2π}{λ}[/itex]x
i know the amplitude is 2mm which is half the max amplitude.
[itex]\frac{A}{2}[/itex]=Asin[itex]\frac{2π}{λ}[/itex]x

So that gives
0.5=sin[itex]\frac{2π}{λ}[/itex]x
[itex]\frac{π}{6}[/itex]=[itex]\frac{2πx}{λ}[/itex]

0.25=x
Now the other partical will be 1.25m from the node.

so the difference is 1m

but the answer given is 50cm
Where i have gone wrong??
 

Answers and Replies

  • #2
199
15
I believe your solution is correct, the answer given is wrong. for a normal traveling wave the answer would be would be 50cm but this is a standing wave (n=1) with nodes at its two ends so I believe your answer is correct!!!
 

Related Threads on Standing waves, find distance

  • Last Post
Replies
1
Views
12K
Replies
7
Views
3K
Replies
1
Views
2K
Replies
5
Views
3K
Replies
1
Views
4K
  • Last Post
Replies
9
Views
3K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
3
Views
1K
Top