Question

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

Answer 1

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,

$(\omega t-kx)=1$

$\omega t=1$

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

$kx=1$

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