Help me in this problem and show me the steps In each case b

In each case below, find phase and group velocities from v_p = omega /k, v_g = Delta omega / Delta k = (omega_2 - omega_1)/(k-2 - k_1), and decide whether the dispersion is normal (V_p > V-g), anomalous (V-p

Solution

a] wave₁= f(x,t)= y= 2.5 sin(4x-10t)

we have the standard equation as y= y_o sin (kx-wt)
Comparing we get k₁= 4m^-1 and w₁=10 rad/s

V_p1= w/k= 10/4= 2.5 m/s

V_p1= 2.5 m/s

For wave 2= g(x,t)= y= 2.5 sin(4.4x-11t)

Comparing we get k₂= 4.4m^-1 and w₂=11 rad/s

V_p2= w/k= 11/4.4= 2.5 m/s

V_p2= 2.5 m/s

V_g= dw/dk= [ w₂-w₁]/[k₂-k₁]=[11-10]/ [ 4.4-4]=1/0.4= 2.5 m/s

V_g= 2.5 m/s

here Vp1= Vp2= Vg, Hence Dispersion is absent