Question

The displacement of a progressive wave is represented by y = A sin($\omega t - kx$) where x is distance and t is time

The dimensions of $\frac{\omega}{k}$are same as those of

• A. Velocity
• B. Wave number
• C. Wavelength
• D. Frequency

Answer 1

Answer: (A)

Velocity

Answer 2

y = A sin $(\omega t - kx)$

As ($\omega t - kx$) represent an angle which is dimensionless,

Therefore, $\lbrack\omega\rbrack = \frac{1}{\lbrack t\rbrack} = \lbrack T^{- 1}\rbrack$ and $[ \mathrm { k } ] = \frac { 1 } { [ \mathrm { x } ] } = [ \mathrm { L } - 1 ]$ $\left\lbrack \frac{\omega}{k} \right\rbrack = \frac{\lbrack T^{- 1}\rbrack}{\lbrack L^{- 1}\rbrack} = \lbrack LT^{- 1}\rbrack$ =Velocity