Question

Two travelling waves produce a standing wave represented by the 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.

पर्याय

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Answer 1

Two travelling waves produce a standing wave represented by the 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 = 1 cm.

Explanation:

By comparing the given equation to the standing wave equation y = 2A cos kx sin ωt

Amplitude R = 2A cos kx

Given equation, y = 1.0 mm cos(1.5 cm^-1) x sin(78.5)s^-1)t

Comparing cos term,

k = `1.57 = (2pi)/lambda`

`lambda = (2pi)/1.57` cm

`lambda/4` is the closest node position to the origin.

= `(2pi)/(4 xx 1.57) = 1` cm