Two waves in one string are described by the wave functions: y1=(3.0cm)cos⁡(4.0x−1.6t) y2=(4.0cm)sin⁡(5.0x−2.0t) where y and x are in centimeters and t is inseconds. Find the superposition of the waves y1+y2 at the points x= 0.500, t=0.

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Two waves in one string are described by the wave functions:  y1=(3.0cm)cos⁡(4.0x−1.6t)  y2=(4.0cm)sin⁡(5.0x−2.0t)  where y and x are in centimeters and t is inseconds. Find the superposition of the waves y1+y2 at the points  x= 0.500, t=0.

Ella Williams · Accepted Answer

given two waves are described as y1=(3.0cm)cos⁡(4.0x−1.6t)&amp;amp;y2=(4.0cm)sin⁡(5.0x−2.0t) At x= 0.500, t=0 we have y=y1+y2 =(3.0cm)cos⁡(4.0⋅0.5−1.6⋅0)+(4.0cm)sin⁡(5.0⋅0.5−2.0⋅0) =- 1.248 + 2.394 =1.146cm

xandir307dc · Accepted Answer

Superposition of waves at x=0.500 and t=0 is,  y=[3.0cos⁡(4.0x−1.6t)]+[4.0sin⁡(5.0x−2.0t)]  =[3.0cos⁡(4.0(0.5)−1.6(0))]+[4.0sin⁡(5.0(0.5)−2.0(0))]  =[3.0cos⁡(2)]+[4.0sin⁡(2.5)]  =-1.15cm

alenahelenash · Accepted Answer

Step 1 We need to find superposition of the waves: y1=(3cm)cos⁡(3x−1.6t) y2=(4cm)sin⁡(5x−2t) Resultant wave is: y=y1+y2 Step 2 Calculation Let us calculate resultant wave at the point x=0.5cm, t=0s: y=y1+y2 =(3cm)cos⁡(4x−1.6t)+(4cm)sin⁡(5x−2t) =(3cm)cos⁡(4×0.5cm−1.6×0s)+(4cm)sin⁡(5×0.5cm−2×0s) y=-1.15cm

Two waves in one string are described by the wave

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