Question

What is the minimum distance between a node & an antinode in a standing wave?

(a) λ

(b) λ/2

(c) 2λ

(d) λ/4

The question was posed to me in an international level competition.

This interesting question is from Reflection of Waves topic in division Waves of Physics – Class 11

Answer 1

Correct answer is (d) λ/4

Explanation: The amplitude in a standing wave is given by Asin(kx).   

Node is a point where amplitude is zero and antinode is a point where amplitude is maximum.

For a node, sin(kx) = 0

kx = 2nπ OR (2π/λ)x = nππ

x = nλ/2.

For an antinode, sin(kx) = 1

kx = (2n+1)π/2

(2π/λ)x = (2n+1)π/2

x = (2n+1) λ/4.

∴ node is at λ/2, λ, 3λ/2 …

& antinode at λ/4, 3λ/4, 5λ/4 …   

∴ minimum distance = λ/2 – λ/4 = λ/4.