Question

The equation of a wave is given by $Y = A$ sin $\omega\left( \frac{x}{v} - k \right)$ where $\omega$ is the angular velocity and $v$ is the linear velocity. The dimension of k is

• A. $LT$
• B. $T$
• C. $T^{- 1}$
• D. $T^{2}$

Answer 1

Answer: (B)

$T$

Answer 2

According to principle of dimensional homogeneity $\lbrack k\rbrack = \left\lbrack \frac{x}{v} \right\rbrack$ = $\left\lbrack \frac{L}{LT^{- 1}} \right\rbrack = \lbrack T\rbrack$.