A transverse harmonic wave travels on a rope according to the following expressi

ID: 1304409 • Letter: A

Question

A transverse harmonic wave travels on a rope according to the following expression:

y(x,t) = 0.12sin(2.7x + 17.9t)

The mass density of the rope is ? = 0.127 kg/m. x and y are measured in meters and t in seconds.

What is the wavelength of the wave?

What is the speed of the wave?

What is the tension in the rope?

At x = 3.3 m and t = 0.41 s, what is the velocity of the rope? (watch your sign)

At x = 3.3 m and t = 0.41 s, what is the acceleration of the rope? (watch your sign)

What is the average speed of the rope during one complete oscillation of the rope?

a.)lambda=2pi/k=2*pi/2.7= 2.327 m

speed=v=w/k=17.9/2.7=6.63 m/s

v=sqrt(T/u)

So T=u*v^2=0.127*6.63^2 = 5.582 N

v=17.9(0.12)cos(2.7*3.3 + 17.9*0.41)= 2.062 m/s

a=-17.9^2(0.12)sin(2.7*3.3 + 17.9*0.41)= - 10.76 m/s^2

average speed=2S/pi

where S=max.speed= 17.9*0.12=2.148 m/s

So average speed during one complete cycle = 2*2.148/pi = 1.367 m/s

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