Two waves travel simultaneously through the same medium. The first wave is descr

Question

Two waves travel simultaneously through the same medium. The first wave is described by y1(x,t) = (2.00 cm)cos[kx-t] and the second wave by y2(x,t) = (3.00 cm)cos(kx-t+). If the resulting wave has an amplitude 4.00 cm, what is a possible value of ? Two waves travel simultaneously through the same medium. The first wave is described by y1(x,t) = (2.00 cm)cos[kx-t] and the second wave by y2(x,t) = (3.00 cm)cos(kx-t+). If the resulting wave has an amplitude 4.00 cm, what is a possible value of ?

1.32 rad

0.833 rad

0.644 rad

0.250 rad

0.782 rad

Explanation / Answer

y1 = (2.00 cm)cos[kx-t]
y2 = (3.00 cm)cos(kx-t+)
y10 = 2 cm, y20 = 3 cm
The amplitude of the resultant wave, Y0 = Sqrt [y102 + y202+ 2y10 y20 cos()]
Y02 = y102 + y202+ 2y10 y20 cos()
Substituting,
42 = 22 + 32 + 2 x 2 x 3 x cos()
cos() = 0.25,
= cos-1(0.25) = 1.32 rad

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