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Question

Particle displacements (in cm) in a standing wave are given by y(x,t)=2sin(0.1πx)cos(100 πt). The distance between a node and the next antinode is

A
2.5 cm
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B
5.0 cm
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C
7.5 cm
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D
10.0 cm
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Solution

The correct option is B 5.0 cm
General expression for a transverse standing wave :
y=Asin(kx)cos(ωt)
Comparing with given equation,
kx=2πxλ=0.1πx
λ=20 cm

The distance between a node and the next antinode =λ4=204=5 cm.
Hence, the correct choice is (b).

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