A transverse traveling wave on a cord is represented by D = 0.22sin(5.6x+34t) where D and x are in meters and t is in seconds. For this wave determine (a) the wavelength, (b) frequency, (c) velocity (magnitude and direction), (d) amplitude, and (e) maximum and minimum speeds of particles on the cord.
d)What is the ratio of density for the different sections of a rope (thin on the left with downward reflected pulse, thick on the right with upward (like a wave) transmitted pulse) to create a 1/2*[wavelength] on the right?
D(x,t) = Asin(kx-εt)
D = 0.22sin(5.6x+34t) where D and x are in meters and t is in seconds
v = Γ/T
T = 1/f
Γ = 2L/n where n = 1 represents fundamental; n = 2 is the second harmonic; etc.
The Attempt at a Solution
Looking at the base formula for a standing wave, I have concluded the following:
a) The wavelength ε = 34 m
b) The frequency f = 5.6 Hz
c) v = Γ/T
T = 1/f = 1/5.6Hz = 0.179 s
Γ = 2L/n >>> Would we assume n = 1? Would we also assume that Length = A = 0.22?
Γ = 2(0.22) = 0.44 m
v = 0.44/0.179 = 2.46 m/s to the right (since Amplitude is positive and it is only a sine function) (how would I find magnitude?)
d) A = 0.22 m
e) Would this be ±v = ±2.46 m/s?
d) How do I go about this?
Thank you for any help!