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.