Answer
No resultant wave is produced in this case. So the resultant amplitude is $0$.
Work Step by Step
The given four waves are:
$y_1(x, t)= (4.00\;mm)\sin(2\pi x-400pt)$
$y_2(x, t)=(4.00\;mm)\sin(2\pi x-400\pi t+0.7\pi)$
$y_3(x, t)=(4.00 mm)\sin(2\pi x-400\pi t +\pi)$
or, $y_3(x, t)=-(4.00 mm)\sin(2\pi x-400\pi t)$
$y_4(x, t)=(4.00\;mm) \sin(2\pi x-400\pi t+1.7\pi)$
Now,
$y_1(x, t)+y_3(x, t)=0$
$y_1(x, t)+y_3(x, t)+y_2(x, t)=(4.00\;mm) \sin(2\pi x-400\pi t+0.7\pi)$
$y_1(x, t)+y_2(x, t)+y_3(x, t)+y_4(x, t)=(4.00\;mm) \sin(2\pi x-400\pi t+0.7\pi)+(4.00\;mm) \sin(2\pi x-400\pi t+1.7\pi)$
or, $y_1(x, t)+y_2(x, t)+y_3(x, t)+y_4(x, t)=(4.00\;mm)[\sin(2\pi x-400\pi t+0.7\pi)+ \sin(2\pi x-400\pi t+1.7\pi)]$
or, $y_1(x, t)+y_2(x, t)+y_3(x, t)+y_4(x, t)=(4.00\;mm)[\sin\Big(\frac{2\pi x-400\pi t+0.7\pi+2\pi x-400\pi t+1.7\pi}{2}\Big)\cos\Big(\frac{2\pi x-400\pi t+0.7\pi-2\pi x+400\pi t-1.7\pi}{2}\Big)$
or, $y_1(x, t)+y_2(x, t)+y_3(x, t)+y_4(x, t)=(4.00\;mm)[\sin(2\pi x-400\pi t+1.2\pi)\cos(0.5\pi)$
or, $y_1(x, t)+y_2(x, t)+y_3(x, t)+y_4(x, t)=(4.00\;mm\cos(0.5\pi))[\sin(2\pi x-400\pi t+1.2\pi)$
or, $y_1(x, t)+y_2(x, t)+y_3(x, t)+y_4(x, t)=0$
Thus, no resultant wave is produced in this case. So the resultant amplitude is $0$.
