Two travelling waves produce a standing wave represented by equation, y = 1.0 mm cos(1.57 cm ⁻¹) x sin(78.5 s ⁻¹)t. The node closest to the origin in the region x > 0 will be at x =.............. cm. Numerical answer type. Work it out, then open the answer.

Answer: 1. Nodes where cos (1.57x) = 0, i.e. 1.57x = π/2 for the first node. x = (1.57)/(1.57) = 1 cm.

Two travelling waves produce a standing wave represented by equation… | JEE Main 2021 (26 Aug, Shift 1)

Q75JEE Main 2021 · 26 AUG · SHIFT 1Easy

Stationary Waves & Vibrating Strings

Two travelling waves produce a standing wave represented by equation,

y = 1.0 mm cos(1.57 cm ${}^{-1}$ ) x sin(78.5 s ${}^{-1}$ )t.

The node closest to the origin in the region x > 0 will be at x = .............. cm.

Numerical answer type. Work it out, then open the answer.

Show answer and solution

Answer: 1

Nodes where $\cos(1.57x) = 0$ , i.e. $1.57x = \frac{\pi}{2}$ for the first node.
$x = \frac{1.57}{1.57} = 1\text{ cm}$ .

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