Consider a progressive wave whose displacement at distance x and time t is y=Asin(. ω t - k x .) . If p=(ω /k) , then the dimensions p are equivalent to:

Question

Consider a progressive wave whose displacement at distance x and time t is y=Asin(. ω t - k x .) . If p=(ω /k) , then the dimensions p are equivalent to: (A) velocity (B) wave number (C) wavelength (D) frequency

Tardigrade Admin · Accepted Answer

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

Q. Consider a progressive wave whose displacement at distance $x$ and time $t$ is $y = A s in (ω t - k x)$ . If $p = \frac{ω}{k}$ , then the dimensions $p$ are equivalent to:

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
$[ω] = \frac{1}{( t )} = [T^{- 1}] an d [k] = \frac{1}{[ x ]} = [L^{- 1}]$
$[\frac{ω}{k}] = \frac{[ ] T ^{- 1}}{[ L ^{- 1} ]} = [L T^{- 1}] = v e l oc i t y$

Q. Consider a progressive wave whose displacement at distance x and time t is y=Asin(ωt−kx) . If p=kω​ , then the dimensions p are equivalent to: