Questions

# Two waves travelling in opposite directions produce a standing wave. The individual wave functions are given by , where x and y are in cm (sin 6.9c = 0.58)

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a
The maximum displacement of the motion at x = 2.3 cm is 4.63 cm.
b
The maximum displacement of the motion at t = 2.3 s is 4.63 cm.
c
Nodes are formed at x values given by 0, π/3, 2π/3,π ,4π/3, ….
d
Antinodes are formed at x values given by π/6, π/2, 5π/6, 7π/6, …

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detailed solution

Correct option is A

y=y1+y2y=4[sin⁡(3x−2t)+sin⁡(3x+2t)]y=4[2sin⁡(3x)cos⁡(2t)]y=8sin⁡(3x)cos⁡(2t)y=Rcos⁡(2t)R=Resultant⁡ Amplitude =8sin⁡(3x)R=8sin⁡[3(2.3)]R=8sin⁡(6.9)R=4.63cmNodes are formed at points of zero intensity, i.e.,             IR=R2=0sin2⁡(3x)=0sin⁡(3x)=03x=0,π,2π,3π,4π,…x=0,π3,2π3,π,4π3,…Antinodes are formed in between.

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Which of the following functions represent a stationary wave? Here a, b and c are constants: