A RoP1 under a tension of 150 N and fixed both ends oscillat

A R_oP_1 under a tension of 150 N and fixed both ends oscillates in a third - harmonic standing wave pattern. The displacement : y=0.10m(sinpiex/2) sin 12 pie t what is the speed of the two waves? What is the length of the Rop? What is the mass of the rope?

Solution

a)

Comparing the given function with

Y(x,t) =2ASin(Kx)Cos(Wt)

=>2A=0.1 =>A=0.05 m

=>K=pi/2

=>W=12pi rad/s

since 2pif =12pi

f=6 Hz

Speed of wave

V=f*lambda =6*4

V=24 m/s

b)

Since wave number is

K=2pi/lambda =pi/2

lambda =4 m

For a nth harmonic

lambda=2L/n

For a third harmomic

lambda =(2/3)L =4

L=6 m

c)

since speed of wave

V=sqrt[T/u]

24 =sqrt[150/u]

=>u =0.26 kg/m

since u=m/L =0.26

m=6*0.26

m=1.5625 kg