The correct option is B 3
Given that, equation of standing wave is
y=5sin(πx3)cos(40πt)
Comparing this with
y=2Asin(2πxλ)cos(2πtT)
we get, λ=6 cm ; T=120 sec
Position of a node on the string is given by x=nλ2, where n=0,1,2,3,4.....
Seperation between two consecutive nodes is given by
Δx=∣∣∣nλ2−(n−1)λ2∣∣∣=λ2
From the given data,
Δx=62=3 cm
Alternate method :
At the nodes, the value of x is such that y=0.
To make sin function zero,
πxn3=nπ
For n=0,x0=0 cm
For n=1,x1=3 cm
∴ seperation between two consecutive nodes is Δx=|x1−x0|=3 cm
Hence, option (b) is the correct answer.