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The stationary waves set up on a string have the equation:
$y = (2 mm) \sin [(6 .28 m^{- 1}) x] \cos ωt$
The stationary wave is created by two identical waves, of amplitude A each, moving in opposite directions along the string. Then:

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A = 2 mm

A = 1 mm

the smallest length of the string is 50 cm

the smallest length of the string is 2 m

answer is B, C.

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Detailed Solution

Comparing with the equation

$y = 2 A \sin (\frac{nπx}{L}) \cos (ωt), we have 2 A = 2 mm or A = 1 mm$

$and \frac{nπx}{L} = 6 .28 x = 2 πx$

$L = \frac{n}{2} m$

for $n = 1, L = 0 .5 m$

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