Maill 5:17 PM 18% a edugen.wileyplus.com WileyPLUS Chapter 16, Problem 052 A rop

Question

Maill 5:17 PM 18% a edugen.wileyplus.com WileyPLUS Chapter 16, Problem 052 A rope, under a tension of 253 N and fixed at both ends, oscillates in a second-harmonic standing wave pattern. The displacement of the rope is where- at one end of the rope, x is in meters, and is in seconds. What are (a) the length of the rope, (b) the speed of the waves on the rope, and (c) the mass of the rope? (d) If the rope oscillates in a third- harmonic standing wave pattern, what will be the period of oscillation? Revlew ResutsyStuy a) Number

Explanation / Answer

F = 253 N
y = 0.398* (sin((?*x)/3)) * sin( 12 ?*t)
y = 2A sin (k*x) * sin (? * t)

a) in a second-harmonic, the wave length = the length of the rope
k = 2?/? = ?/3 --> ? = 6 m
The length of the rope L = 6 m

b) The sped of the waves
v = ?/k = 12?/(?/3) = 36 m/s

c) melde's law :
v = ?(F *L/m)
--> m = F * L/v^2
=253 * 12/(36)^2
= 2.34 kg

d)in a third-harmonic :
L = 1.5 ? ---> ? = 6/1.5 = 4 m
v = ?/T --> T = ?/v = (6/1.5)/36 = 0.111 s

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