Combining Stanting Waves. A guitar string of length L is plucked in such a way t
ID: 1729169 • Letter: C
Question
Combining Stanting Waves. A guitar string of length L is plucked in such a way that thetotal wave produced is the sum of the fundamental and the secondharmonic. That is, the standing wave is given by y(x,t) = y1(x,t) + 2(x,t) Where y1(x,t) =Csin1tsink1x y2(x,t) =Csin2tsink2x With 1 = vk1 and2 = vk2, a) At what values of x are the nodes of y1? b) At what values of x are the nodes of y2? c) Graph the total wave at t =0, t=1/8f1, t= 1/4f1, t=3/8f1,and t= 1/2f1. d) Does the sum of the two standing waves y1 andy2 produce a standing wave? Explain. Combining Stanting Waves. A guitar string of length L is plucked in such a way that thetotal wave produced is the sum of the fundamental and the secondharmonic. That is, the standing wave is given by y(x,t) = y1(x,t) + 2(x,t) Where y1(x,t) =Csin1tsink1x y2(x,t) =Csin2tsink2x With 1 = vk1 and2 = vk2, a) At what values of x are the nodes of y1? b) At what values of x are the nodes of y2? c) Graph the total wave at t =0, t=1/8f1, t= 1/4f1, t=3/8f1,and t= 1/2f1. d) Does the sum of the two standing waves y1 andy2 produce a standing wave? Explain. d) Does the sum of the two standing waves y1 andy2 produce a standing wave? Explain.Explanation / Answer
y(x,t) = y1(x,t) + 2(x,t) Where y1(x,t) =Csin1tsink1x y2(x,t) =Csin2tsink2x With 1 = vk1 and2 = vk2,a) At what values of x are the nodes of y1?
sink1x = 0, x = n/k1 b) At what values of x are the nodes of y2?
sink2x = 0, x = m/k2
a) At what values of x are the nodes of y1?
sink1x = 0, x = n/k1 b) At what values of x are the nodes of y2?
sink2x = 0, x = m/k2