The equation of a wave is given by Y=A sin ω((x/v)-k), where ω is the angular velocity, x is the displacement and v is the linear velocity. The dimensions of k is

Question

The equation of a wave is given by Y=A sin ω((x/v)-k), where ω is the angular velocity, x is the displacement and v is the linear velocity. The dimensions of k is (A) [LT] (B) [T] (C) [T-1] (D) [T2]

Tardigrade Admin · Accepted Answer

ω[(x/v)-k] is dimensionless and unit of (x/v) is same as k . So, dimensions of k=([x]/[v])=([L]/[LT-1])=[T]

Q. The equation of a wave is given by $Y = A s in ω (\frac{x}{v} - k)$ , where $ω$ is the angular velocity, $x$ is the displacement and $v$ is the linear velocity. The dimensions of $k$ is

$[L T]$

$[T]$

$[T^{- 1}]$

$[T^{2}]$

$ω [\frac{x}{v} - k]$ is dimensionless and unit of $\frac{x}{v}$ is same as $k$ .
So, dimensions of $k = \frac{[ x ]}{[ v ]} = \frac{[ L ]}{[ L T ^{- 1} ]} = [T]$

Q. The equation of a wave is given by Y=Asinω(vx​−k), where ω is the angular velocity, x is the displacement and v is the linear velocity. The dimensions of k is

[LT]

[T]

[T−1]

[T2]