Physics

In the equation y = A sin $$ (\omega  - Kx) $$, obtain the dimensional formula of $$ \omega $$ and K.Given x is distance and t is time.


SOLUTION

In the given equation $$y=A\sin (\omega t-kx)$$

Since, trigonometric function is a dimensionless quantity. So, $$(\omega t-kx)$$is also dimensionless quantity.

So,

$$ (\omega t-kx)=1 $$

$$ \omega t=1 $$

$$ \left[ \omega  \right]=\dfrac{1}{\left[ T \right]}={{\left[ T \right]}^{-1}} $$

$$ kx=1 $$

$$ \left[ k \right]=\dfrac{1}{\left[ L \right]}={{\left[ L \right]}^{-1}} $$

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