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-p.CShttps://www.webassign.net/web/Student, ignment-Responses/submit?dep=13643207 8. +19 points TipMod6 5.P017. My Notes + Ask Your Teacher Two harmonic waves travel simultaneously along a long wire. Their wave functions are y1 = 0.002 cos(8.0x-400t) and y2 = 0.002 cos(7.7-328t), where y and x are in meters and t in seconds. (a) Write the wave function for the resultant wave in the form of the equation below. 1/m rad/s 1/m rad/s Ak (b) What is the phase velocity of the resultant wave? m/s (c What is the group velocity? m/s (d) Calculate the range between successive zeros of the group.

Solution

Y=Y₁+Y₂ = 0.002[Cos(8x-400t)+Cos(7.7x-328t)]

Since CosA+CosB =2Cos(A+B/2)Cos(A-B/2)

Y=0.002*2*Cos(15.7x-728t/2)Cos(0.3x-72t/2)

Y=0.004Cos[(1/2)0.3x-(1/2)72t]Cos[7.85x-364t]

Comparing this with given equation

Y_o=0.004/2=0.002 m

dK =0.3 m^-1

dW=72 rad/s

k=7.85 m^-1

W=364 rad/s

b)

Phase velocity

V_p =W/K =364/7.85

V_p = 46.37 m/s

c)

Group velocity

V_g = dW/dK =72/0.3

V_g = 240 m/s

d)

For Some instant of time t,there will be zero in

0.15x₁ = pi/2 and 0.15x₂=3pi/2

0.15*dX =pi

dX=6.67pi

e)

dX=6.67pi*0.3/dK

dX=2pi/dK