How Do You Calculate Node Distance in a Standing Wave?

[nil1996]

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\frac{2π}{λ}x
i know the amplitude is 2mm which is half the max amplitude.
\frac{A}{2}=Asin\frac{2π}{λ}x

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

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

so the difference is 1m

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

 

[NihalSh]

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!