The displacement y of a particle in a medium can be expressed as  y=10−6sin⁡100t+20x+x4 , wheret is in second and x in metre. The speed of the wave is

The displacement is given by y=10−6sin⁡100t+20x+π4Comparing with standard equation y=Asin⁡(ωt+kx+ϕ)we get   ω=100,k=20where, ω  is angular frequency and k is angular wave number.Now,    k=2πλ=2πvλv=ωv=20⇒ v=ω20=10020=5ms−1So, the speed of the wave is 5 ms-1.