Answer to Question #117801 in Mechanics | Relativity for Hadi ezzeddine

Question

Which of the following wave functions represents the resultant wave due to the interference between the two waves:
y_result (x,t) = 4 sin⁡(2πx ‒ 20πt + φ)
y_result (x,t) = 2 sin⁡(πx ‒ 10πt + φ/2)
y_result (x,t) = 4 cos⁡(φ/2) cos⁡(πx ‒ 10πt - φ/2)
y_result (x,t) = 4 cos⁡(φ/2) sin⁡(2πx ‒ 20πt + φ/2)
y_result (x,t) = 2 sin⁡(φ/2) sin⁡(2πx ‒ 20πt + φ/2)
Other:

Answer 1

$y1(x,t)=Asin(kx−ωt+φ)\\,y2(x,t)=Asin(kx−ωt).$

resultant will be :

$2Asin(kx−ωt+\fracφ2)cos(\fracφ2).$