Transverse waves traveling on a string and standing waves
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Two transverse waves traveling on a string combine to a standing wave. The displacements for the traveling waves are Y1(x,t) =0.0160 sin (1.30m^-1 x - 2.50 s^-1t +.30). Y2(x,t) = .0160 sin (1.30m^-1 x +2.50s^-1 + .70), respectively, where x is position along the string and t is time.
A. Find the location of the first antinode for the standing wave at x> 0.
B. Find the first t>0 instance when the displacement for the standing wave vanishes everywhere.
Well, I really tried to figure this out. First I set the two waves to the standard standing wave Y(x,t) = 2Asinkx(sinwt) =2(0.0160)sin1.30m^-1x(sin2.50s^-1t)
I first tried to find the wavelength then since the first node that is >x is lambda/2
I found that node and then divided the answer in half. But that was wrong.
For part b, I was looking in my text book and it had a figure that suggested to me that when the standing wave vanishes it is when t= (8/16)T. I tried to find T then use that to solve for t but I was wrong. Am I totally off base?
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The solution provides very detailed solution to this problem using trigonometry to find the wave function of two super imposed waves.
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Two transverse waves traveling on a string combine to a standing wave. The displacements for the traveling waves are Y1(x,t) =0.0160 sin (1.30m^-1 x - 2.50 s^-1t +.30). Y2(x,t) = .0160 sin (1.30m^-1 x +2.50s^-1 + .70), respectively, where x is position along the string and t is time.
A. Find the location of the first antinode for the standing wave at x> 0.
B. Find the first t>0 instance when the displacement for the standing wave vanishes everywhere.
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