The correct option is B 16 cm , 32 cm
Given,
The pressure wave is
p=5sin(2πx32)cos(50πt)
General equation for pressure wave in a closed organ pipe is
p=−2pocos(2πλx)sin(2πTt)
Comparing both equations, we get
k=2πλ=2π32
⇒λ=32 cm
Positions of zero pressure variation (or pressure nodes) are given by
x=nλ2 where n=0,1,2,3....
∴x=0 , λ2 , λ , 3λ2......
∵λ=32 cm
we can conclude that,
For, n=0 , x=0 cm
n=1 , x=16 cm
n=2 , x=32 cm
n=3 , x=48 cm
So, among the given options, only option (b) satisfies the position of pressure node.