When a transverse wave travels in a medium, the displacement (y) of a particle located at x at time t is given by y = a sin ( bt − cx ) where a, b and c are constants.

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The argument of sine must be dimensionless, and the amplitude a has the same dimension as y.

So $[a] = [y]$ ; statement (A) is correct.

$b t$ is dimensionless, so $[b] = [T^{- 1}]$ ; its SI unit is $s^{- 1}$ , not second. (B) is wrong.

$c x$ is dimensionless, so $[c] = [L^{- 1}] = [M^{0} L^{- 1} T^{0}]$ , not $[M^{0} L^{- 1} T^{- 1}]$ . (C) is wrong.

$[\frac{b}{c}] = \frac{[ T ^{- 1} ]}{[ L ^{- 1} ]} = [L T^{- 1}]$ , the dimension of velocity. (D) is correct.

Physics - Wave on String Question with Solution | TestHub

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