Physics - Unit & Dimension Question with Solution | TestHub

Here, $y=a\sin (bt-cx)$ Compar ing this equation with geneal wave equation $$y=a\sin \left(\frac{2\pi t}{T}-\frac{2\pi x}{\lambda }\right)$$ we get $b=\frac{2\pi }{T},c=\frac{2\pi }{\lambda }$ (a) Dimensions of $\frac{y}{a}=\frac{[L]}{[L]}=$ Dimensionless (b) Dimensions of $bt=\frac{2\pi }{T}\cdot t=\frac{[T]}{[T]}$ $=$ Dimensionless (c) Dimensions of $cx=\frac{2\pi }{\lambda }\cdot x=\frac{[L]}{[L]}$ $=$ Dimensionless (d) Dimensions of $\frac{b}{c}=\frac{\frac{2\pi }{T}}{\frac{2\pi }{\lambda }}=\frac{\lambda }{T}=\left[L{T}^{-1}\right]$