Consider two sinusoidal waves traveling along a string, modeled as y1(x, t) = (0.4 m)sin[(3 m−1)x + (2 s−1)t] and y2(x, t) = (0.8 m)sin[(6 m−1)x − (5 s−1)t]. What is the vertical displacement (in m) of the resultant wave formed by the interference of the two waves at the position x = 0.9 m at time t = 0.4 s? (Indicate the direction with the sign of your answer.)

y(x,t)=-0.395m

Explanation:

The wave function modeling waves are:

= (0.4 m)sin[(3 )x + (2 )t]

=(0.8 m)sin[(6  )x − (5 )t]

The principle of superposition can be defined as the resultant of and is equal to their algebraic sum

y(x,t)= (0.4 m)sin[(3 )x + (2 )t] + (0.8 m)sin[(6  )x − (5 )t]

Substitute 0.9m for x and 0.4s for t as required  

y(x,t)= (0.4 )sin[(3 )(0.9) + (2 )(0.4)] + (0.8 m)sin[(6  )(0.9)− (5 )(0.4)]

y(x,t)= -0.14 - 0.255

y(x,t)=-0.395m

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