In the relation y=rsin⁡(ωt−kx), the dimensions of ω/k are

y=rsin⁡(ωt−kx) Here ωt= angle ⇒ω=1T=T−1 Similarly, kx= angle ⇒k=1x=L−1 ∴ ωk=T−1L−1=LT−1Or simply ω/k represents wave velocity.ωk=2πf2π/λ=fλ=v, where f is frequency.