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 + 27 t). x and y are in m; t is in s.

calculate the average power transmitted by the string. Data: mass of a 215 m long piece of the string is 2.35 kg.

Answer 1

the power is calculated as

P = 1/2 * u * w² * A² * v

where u is linear mass density, A is amplitude,

w = 27 rad/sec

A = 0.13 m

u = m/L = 2.35 / 215 = 0.01093 kg/m

v = w / k = 27 / 9 = 3 m/s

so,

P = 1/2 * 0.01093 * 27² * 0.13² * 3

P = 0.20199 W