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Two waves traveling on a string in the same direction both have a frequency of 92 Hz, a wavelength of 0.19 m, and an amplitude...Asked by Samet heelllpp
Two waves traveling on a string in the same direction both have a frequency of 92 Hz, a wavelength of 0.19 m, and an amplitude of 0.32 m. What is the amplitude of the resultant wave if the original waves differ in phase by pi /3 rad?
What is the phase difference between the two waves if the amplitude of the resultant wave is 0.25 m?
What is the phase difference between the two waves if the amplitude of the resultant wave is 0.25 m?
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Answered by
bobpursley
consider your trig
A1 *cos(wt+theta1) + A2 cos(wt+theta2)
= A3 * cos(wt+Theta3)
where
A3^2=(A1cosTheta1 +A2cosTheta2)^2+(A1sinTheta1+A2sinTheta2)^2
and Theta3 is given by
arc tan ( (A1SinTheta1+A2SinTheta2)/(A1cosTheta1+A2CosTheta1) )
A1 *cos(wt+theta1) + A2 cos(wt+theta2)
= A3 * cos(wt+Theta3)
where
A3^2=(A1cosTheta1 +A2cosTheta2)^2+(A1sinTheta1+A2sinTheta2)^2
and Theta3 is given by
arc tan ( (A1SinTheta1+A2SinTheta2)/(A1cosTheta1+A2CosTheta1) )