Question

When a wave transverse in a medium, the displacement of a particle located at distance $x$ at time $t$ is given by $y=asin(bt-cx)$ where $a,b$ and $c$ are constants of the wave. The dimension of $b/c$ is same as that of :

• A. Wave velocity
• B. Wavelength
• C. Wave amplitude
• D. Wave frequency

Answer 1

The correct option is A Wave velocity

Argument of sin is dimensionless and using principle of dimensional homogeneity, we get
$|bt|=|cx|=\left[M^0{L}^0{T}^0\right]$
Thus, $|b|=T^{-1}$ and $|c|=\left[L^{-1}\right]$
Thus, dimensions of $b/c$ are $\left[L{T}^{-1}\right]$, which is same as velocity of wave.