Question

A sine wave on a string is described by the wave function

y (x, t) = 5.50 sin (0.70x-60.00t)

where x and y are in meters and t in seconds. The mass per unit
length of this rope is 11.00 g / m. Determine (a) the wavelength,
(b) the average power transmitted by the wave.

a |
8.98 m, 95464.29 W |

b |
0.10 m, 212.14 W |

c |
0.10 m, 95464.29 W |

d |
8.98 m, 212.14 W |

Answer #1

**compare the given equation with standard
equation**

**y(x,t) = A*sin(k*x - w*t)**

**A = 5.5 m
k = 0.7 rad/m
w = 60 rad/s**

**a) we know, k = 2*pi/lamda**

**lamda = 2*pi/k**

**= 2*pi/0.7**

**= 8.98 m**

**b) power transmitted by string wave,**

**P = (1/2)*mue*w^2*A^2*v**

**here**

**mue --> linear mass density of the string
w --> angular frequency
A---> amplitude
v - --> wave velocity on te string.**

**P = (1/2)*mue*w^2*A^2*(w/k)**

**= (1/2)*11*10^-3*60^2*5.5^2*(60/0.7)**

**= 95400 W**

**so, option a is the correct answer.**

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