Physics: Stretched strings question?

The figures below show a stretched string vibrating in several of its modes. If the length of the string is 2.0m, what is the wavelength of the wave on the string in (a), (b), (c), (d)?





Picture: http://i25.tinypic.com/2l89mwy.jpg

Physics: Stretched strings question?
a) N O .......... L .............. O N(node)


distance = node to node =λ/2 = L = 2


λ = 4 meter


b) N to N + N to N = λ/2 + λ/2 = 2λ/2


2*λ/2 = 2 %26gt;%26gt; λ = 2 meter


c) 3*λ/2 = 2 %26gt;%26gt; λ = 4/3 = 1.333 meter


c) 4*λ/2 = 2 %26gt;%26gt; λ = 1 meter
Reply:In each step the wave length increases in steps of λ/2.


a ) the length of string = λ/2


b) the length of string = λ/2 + λ/2 = 2 *λ/2


c} the length of string = λ/2 + λ/2 + λ/2 = 3*λ/2


d) the length of string = λ/2 + λ/2+ λ/2 +λ/2


= 4*λ/2
Reply:a)


Two nodes are show and distance between two nodes is λ/2 .


So λ = (2x2) = 4 m





b) λ = 2 m





c) 1.5λ is shown





1.5λ = 2


λ = 4/3 m





d) 2λ = 2


λ = 1 m