A fellow student of mathematical bent tells you that the wave function of a trav

Question

A fellow student of mathematical bent tells you that the wave function of a traveling wave on a thing rope is y(x,t) = 2.10mm cos[(7.05rad/m)x + (746rad/s)t]. Being more practical-minded, you measure the rope to have a length of 1.33m and a mass of 3.40g.

A) Determine the amplitutde.

B) Determine the frequency.

C) Determine the wavelength.

D) Determine the wave speed.

E) Determine the direction the wave is traveling. (+x or -x)

F) Determine the tension in the rope.

G) Determine the average power transmitted by the wave.

Explanation / Answer

The wave function of a traveling wave on a thin rope is y(x,t)= 2.10mm cos[( 7.05 rad/m)x + (746 rad/s).

Amplitude =A =2.10 mm=0.0021 m

Angular frequency = w =746

frequency = 2pi/746 = 0.0084

Wavelength =2pi/7.05 = 0.891

Mass / length = m =0.0034/1.33=0.002556 kg/m

speed of wave = v =w/k =746 / 7.05 = 105.816 m/s
Tension = T =v^2m= [(105.816 )^2]*0.002556

Tension = T =28.6196 N
the average power transmitted by the wave=(1/2)m*v*w^2*A^2

the average power transmitted =(1/2)0.002556 *105.816*746*746*0.0021*0.0021 =0.3319 W

the average power transmitted by the wave is 0.3319 W

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