The displacement of a progressive wave is represented by y=A sin(ω t-kx) where x is distance and t is time. The dimensions of (ω/k) are same as those of

Question

The displacement of a progressive wave is represented by y=A sin(ω t-kx) where x is distance and t is time. The dimensions of (ω/k) are same as those of (A) velocity (B) wave number (C) wavelength (D) frequency

Tardigrade Admin · Accepted Answer

y=A sin (ω t-kx) As (ω t-kx) represents an angle which is dimensionless, therefore [ω]=(1/[t])=[T-1] and [k]=(1/[x])=[L-1] [(ω/k)]=([T-1]/[L-1])=[LT-1]= velocity

Q. The displacement of a progressive wave is represented by $y = A s in (ω t - k x)$ where $x$ is distance and $t$ is time. The dimensions of $\frac{ω}{k}$ are same as those of

velocity

wave number

wavelength

frequency

$y = A s in (ω t - k x)$
As $(ω t - k x)$ represents an angle which is dimensionless, therefore
$[ω] = \frac{1}{[ t ]} = [T^{- 1}]$ and $[k] = \frac{1}{[ x ]} = [L^{- 1}]$
$[\frac{ω}{k}] = \frac{[ T ^{- 1} ]}{[ L ^{- 1} ]} = [L T^{- 1}] =$ velocity

Q. The displacement of a progressive wave is represented by y=Asin(ωt−kx) where x is distance and t is time. The dimensions of kω​ are same as those of