String The transverse displacement of a stretched string from equilibrium as a f
ID: 1465352 • Letter: S
Question
String The transverse displacement of a stretched string from equilibrium as a function of time and position is given by: y=0.13 cos(3 x + 99 t). x and y are in m; t is in s. False: The wave moves in the positive x direction Greater than: The wavelength is ..... 1 m
Equal to: The speed of the wave is ..... 33 m/s
Less than: The period is ..... 0.1 seconds You are correct.
Calculate the average power transmitted by the string. Data: mass of a 231 m long piece of the string is 2.75 kg
By comparison, =99 rad-S- 99 rad-s -1 99 rad·s* 2 = 33 ms-1 Hence, the speed of the wave is Equal to 33 ms Period is given by the relation, e wave 1s 99 rad-s1 = 0.06 s Hence, periodis Less than 0 I seconds Hence, period is Less than 0.1secondsExplanation / Answer
m/L = 2.75/231
m/L = u = 0.0119 kg/m
E/cycle = 0.5*m/L*omega^2*A^2*wavelength
P = 0.5 * 0.0119 *99* 99 *0.13*0.13*1
P = 0.985 J/cycle
P = E/cycle*f
P = 0.5*m/L*omega^2*A^2*wave velocity
P = 0.5 * 0.0119*99*99*0.13*0.13* 33
P = 32.52 W