The transverse displacement of a stretched string from equilibrium as a function

Question

The transverse displacement of a stretched string from equilibrium as a function of time and position is given by: y=0.13 cos(9 x-99 t). x and y are in m: t is in s. Greater than The wavelength is 1 m Less than The speed of the wave is 12 m/s Greater than The period is 0.1 seconds true The wave travels in the positive x direction A traveling wave can be any function of (2*pi*x/lambda-2*pi*t/period). Calculate the various parameters where needed then select the proper answers. Submit Answer Incorrect. Tries 2/12 Previous Tries Calculate the average power transmitted by the string. Data: mass of a 217 m long piece of the string is 1.71 kg 7.83 W Submit Answer Incorrect. Tries 1/12 Previous Tries

Explanation / Answer

y = 0.13 cos(9x - 99t)

comparing with the general equation we get

w = 99 ; k = 9 ; A = 0.13

1)wavelength is LESS THAN 1 m

since, lambda = 2 pi/k

lambda = 2 pi/9 = 2 x 3.14/9 = 0.698 m

2)The speed is LESS THAN 12 m/s

v = w/k = 99/9 = 11 m/s

3)Period is LESS THAN 0.1 s

T = 2 pi/99 = 0.0634 s

4)TRUE that The wave travels in +X direction.

m = 1.71 kg ; L = 217 m

the energy is:

E = 1/2 m v^2

v = w A = 99 x 0.13 = 12.87

Energy per cycle is:

E/cycle = 1/2 (m/L) v^2 x lambda

E/cycle = 0.5 x 1.71/217 x 12.8^2 x .698 = 0.456 J/cycle

f = 1/T = 1/0.0634 = 15.77 Hz

P = E/cycle x f = 0.456 x 15.77 = 7.19 W

Hence, P = 7.19

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