solve wth values given A rope, under a tension of 370 N and fixed at both ends,

Question

solve wth values given

A rope, under a tension of 370 N and fixed at both ends, oscillates in a second-harmonic standing wave pattern. The displacement of the rope is given below where x = 0 at one end of the rope, x is in meters, and t is in seconds.

y=(.04m)(sin(pix/8))sin18pi(t)

(a) What is the length of the rope? m

(b) What is the speed of the waves on the rope? m/s

c) What is the mass of the rope? kg

(d) If the rope oscillates in a third-harmonic standing wave pattern, what will be the period of oscillation? s

Explanation / Answer

similiar type of answer with same formula etc .. but values r changed just check dis ..helpful for u

F = 360 N
y = 0.58* (sin((%u03C0*x)/10)) * sin( 20 %u03C0*t)
y = 2A sin (k*x) * sin (%u03C9 * t)

a) in a second-harmonic, the wave length = the length of the rope
k = 2%u03C0/%u03BB = %u03C0/10 --> %u03BB = 20 m
The length of the rope L = 20 m

b) The sped of the waves
v = %u03C9/k = 20%u03C0/(%u03C0/10) = 200 m/s

c) melde's law :
v = %u221A(F *L/m)
--> m = F * L/v^2
=360 * 20/(200)^2
= 0.18 kg

d)in a third-harmonic :
L = 1.5 %u03BB ---> %u03BB = 20/1.5 = 13.33 m
v = %u03BB/T --> T = %u03BB/v = (20/1.5)/200 = 0.067 s

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