Two waves on one string are described by the wave functions y1=3.0cos⁡(4.0x−1.6t) y2=4.0sin⁡(50x−2.0t) where x and y are in centimeters and t is in seconds. Find the superposition of the waves y1+y2 at the points (a) x = 1.00, t = 1.00; (b) x = 1.00, t = 0.500; and (c) x = 0.500, t = 0 Note: Remember that the arguments of the trigonometric functions are in radians.

Question

Two waves on one string are described by the wave functions y1=3.0cos⁡(4.0x−1.6t) y2=4.0sin⁡(50x−2.0t) where x and y are in centimeters and t is in seconds. Find the superposition of the waves y1+y2 at the points (a) x = 1.00, t = 1.00; (b) x = 1.00, t = 0.500; and (c) x = 0.500, t = 0 Note: Remember that the arguments of the trigonometric functions are in radians.

unett · Accepted Answer

Step 1   We need to find superposition of the waves:  y1=(3cm)cos⁡(4x−1.6t)  y2=(4cm)sin⁡(5x−2t)  Resultant wave is:  y=y1+y2  Step 2  Calculation:  a) Let us calculate resultant wave at the point x=1cm, t=1s:  y=y1+y2  y1=(3cm)cos⁡(4x−1.6t)+(4cm)sin⁡(5x−2t)  =(3cm)cos⁡(4×1cm−1.6×1s)+(4cm)sin⁡(5×1cm−2×1s)  y=-1.65cm  Step 3  b) Let us calculate resultant wave at the point x=1cm, t=0.5s  y=y1+y2  y1=(3cm)cos⁡(4x−1.6t)+(4cm)sin⁡(5x−2t)  =(3cm)cos⁡(4×1cm−1.6×0.5s)+(4cm)sin⁡(5×1cm−2×0.5s)  y=-6.02cm  c) Let us calculate resultant wave at the point x=0.5cm, t=0s  y=y1+y2  y1=(3cm)cos⁡(4x−1.6t)+(4cm)sin⁡(5x−2t)  =(3cm)cos⁡(4×0.5cm−1.6×0s)+(4cm)sin⁡(5×0.5cm−2×0s)  Result  a) y=-1.65cm;    b) t=-6.02;    c)y=1.15cm;

Two waves on one string are described by the wave functions y_1=3.0\cos(4.0x-

Answered question

Answer & Explanation

New Questions in Trigonometry