First slide

Dimensions of physical quantities

Question

In the relation $y = A \sin (ω t - k x)$ , the dimensions of $ω / k$ are: (y- displacement, A- amplitude, t-time, x-position)

Moderate

A

$[M^{0} L^{0} T^{0}]$
B

$[M^{0} L^{1} T^{- 1}]$
C

$[M^{0} L^{0} T^{1}]$
D

$[M^{0} L^{1} T^{0}]$

Solution

$\begin{array}{l} y = A \sin (ω t - k x) \\ Here ω t = angle \Rightarrow ω = \frac{1}{T} = [T^{- 1}] \\ Similarly, k x = angle \Rightarrow k = \frac{1}{x} = [L^{- 1}] \\ ∴ \frac{ω}{k} = \frac{T^{- 1}}{L^{- 1}} = [M^{0} L T^{- 1}] \end{array}$
Or simply $ω$ /k represents wave velocity.
$\frac{ω}{k} = \frac{2 π f}{2 π / λ} = f λ = v, where f is frequency.$

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