A transverse wave on a rope is given by the following equation, y(x, t) = [(0.80

Question

A transverse wave on a rope is given by the following equation, y(x, t) = [(0.800 cm^-1)x + (200 s^-1)t] Find the amplitude. Find the period. Find the frequency. Find the wavelength. Find the speed of propagation. Sketch the shape of the rope at the following values of t:0, 0.0013 s, and 0.0025 s. (Do this on paper. Your instructor may ask you to turn in this work.) Is the wave travelling in the +x direction or -x direction? The mass per unit length of the rope is 0.500 kg/m. Find the tension. Find the average power of this wave.

Explanation / Answer

compare the given equation with, standard equation

y(x,t) = A*cos(k*x + w*t)

a) Amlitude, A = 0.8 cm

Time period, T = 2*pi/w

= 2*pi/(pi*200)

= 0.01 s

fequency, f = 1/T

= 1/0.01

= 100 hz

wavelength, lamda = 2*pi/k

= 2*pi/(pi*0.35)

= 5.71 cm

v = w/k

= (pi*200)/(pi*0.35)

= 571.4 m/s

b)

c) -x direction

d) given, mue = 0.5 kg/m

we know, v = sqrt(T/mue)

v^2 = T/mue

==> T = v^2*mue

= 571.4^2*0.5

= 285.7 N

e) Average power transimtted, P_avg = 0.5*mue*w^2*A^2*v

= 0.5*0.5*(pi*200)^2*0.008^2*571.4

= 3609 Watts

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