A fellow student of mathematical bent tells you that the wave funcion of a trave

Question

A fellow student of mathematical bent tells you that the wave funcion of a traveling wave on a thin rope is y(x,t) = 2.35mm cos[(6.96rad/m)x + (749rad/s)t]. Being more practical-minded, you measure the rope to have a length of 1.30m and a mass of 3.36g.

a) Amplitude = .00235 m

b) Determine the frequency.
= ? Hz

c) Wavelength = 0.903 m
d) Wave speed = 108 m/s

e) Determine the direction the wave is traveling.
-x direction
+x direction

f) Determine the tension in the rope.
= ? N

g) Determine the average power transmitted by the wave.
= ? W

Explanation / Answer

Here , y (x,t) = 2.35 mm cos[(6.96 rad/m)x + (749 rad/s)t] comparing it with , y(x,t) = A*cos ( w*t + k*x ) a) Amplitude = 0.00235 m b) w = 749 rad/s since , w = 2*pi*f on solving , f = 119.2 Hz c)v = f*lamda lamda = 0.906 m { "v" from "d" part } d) wave speed (v)= coefficient of "t" / coefficient of "x" = 749 / 6.96 = 108 m/s e ) direction of travel = + x direction { since coefficient of "x" is positive } f) u = mass / length = 3.36 / 1.3 = 2.58 kg /m v = sqrt ( T / u ) on solving , T = 30.093 kilo N g) Average power (P) = T.v P = 3250.05 Kilo W

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.