A standing wave is y = 1.0 mm cos(1.57 cm⁻¹ x) sin(78.5 s⁻¹ t). Find the node nearest the origin for x > 0, in cm.
Physics · Wave Motion
JEE Mains 2021

Question

A standing wave is y = 1.0 mm cos(1.57 cm⁻¹ x) sin(78.5 s⁻¹ t). Find the node nearest the origin for x > 0, in cm.

G1 Physics · Accepted Answer

Step 1: Nodes satisfy cos(1.57x)=0. Step 2: The first positive solution is 1.57x=π/2≈1.57, hence x≈1 cm. Final answer: 1 cm.