Question
Given y = a sin (ωt– kx) where 'x' is position and 't' is time. Show that ω/k has dimensions of velocity.
Solution
Here, y = a sin (ωt- kx), where x is position and t is time.
Sine has dimensions of angle, which is dimensionless.
ωt is dimensionless.
And
has the same dimensional formula as that of frequency.
So,
Similarly, kx is dimensionless and dimensions of k are,
Now dimensional formula of,
, which is same as the dimensions of velocity.
Sine has dimensions of angle, which is dimensionless.
ωt is dimensionless. And
has the same dimensional formula as that of frequency. So,
Similarly, kx is dimensionless and dimensions of k are,
Now dimensional formula of,
, which is same as the dimensions of velocity. 
