High School

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Calculate the average power transmitted by the string.

Data: The mass of a 147 m long piece of the string is 2.19 kg.

Answer :

The average power transmitted is 0.08157 W.

How the average power is calculated.

The general equation for the position function is given by :

y = Acosk(kx + wt)

where

A is amplitude

k is spring constant

w is angular acceleration

t is time(period)

x is displacement in x direction

The given equation is

y = 0.13cos(9x + 18t)

Compare the equations

A = 0.13 m

k = 9N/m

w = 18rad/s

The wavelength

λ = 2π/k

= 2* 3.142/9 =

= 0.698 m

Speed of the wave is given as

v = w/k = 18/9

= 2m/s

Mass per unit length

υ = m/L

= 2.19/147

= 0.014897kg/m

Average Power transmitted is given as,

P = 1/2υw²A²v

Substitute into the equation

P = 1/2* 0.014897* 18² * 0.13² * 2

P = 0.08157 W

Thus the average power transmitted is 0.08157 W.

Complete question

The transverse displacement of a stretched string from equilibrium ys o.finctiseo of tims and positio a 's given bys i y 0.13 cos(9 x + 18t). x and y are in m: t is in s.

Greater than: The period is 0.1 seconds. Equal to: The speed of the wave is 2 m/s. The wave travels in the negative x direction. Less than: The wavelength is 1 m. Calculate the average power transmitted by the string. data: mass of a 147 m long piece of the string is 2.19 kg.

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