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 - 81 t). x and y are in m; t is in s. (Q1-4QTrue or False or Greater than or Less than or Equal to)
1. The wave moves in the negative x direction.
2. The speed of the wave is ..... 10 m/s.
3. The wavelength is ..... 1 m.
4. The period is ..... 0.1 seconds.

5. Calculate the average power transmitted by the string. Data: mass of a 197 m long piece of the string is 2.11 kg.

Answer 1

a) true

b)

less than

v = w/k = 81 / 9 = 9 m/s

c)

less than

L = 2pi / 9 = 0.698 m

d)

less than

w = 2pi /T = 81

T = 0.084 s

e)

av power is given by

P = 0.5 (m/L) A^2 w^2 v

P = 0.5* (2.11 / 197)* 0.13^2* 81^2* 9

P =5.344 W