Three waves of equal frequency having amplitudes 13 m , 6 m , 5 m arrive at a given point with successive phase difference of /2 . The amplitude of the resultant wave is (in m ) ( 90^ = 0, = -1)

Step-by-step solution

Let the three waves be represented by phasors A ₁ , A ₂ , and A ₃ . Taking the first wave along the x-axis, the phase angles of the three waves are 0 , /2 , and respectively. The x-component of the resultant amplitude is: R_x = A₁ (0) + A₂ ( /2) + A₃ ( ) R_x = 13(1) + 6(0) + 5(-1) = 13 - 5 = 8 m The y-component of the resultant amplitude is: R_y = A₁ (0) + A₂ ( /2) + A₃ ( ) R_y = 13(0) + 6(1) + 5(0) = 6 m The resultant amplitude R is given by: R = R_x^2 + R_y^2 R = 8^2 + 6^2 = 64 + 36 = 100 = 10 m Answer: 10