For the transverse wave with displacement y=8m sin (2pt/1m x + 4 pt/1s t) what i

Question

For the transverse wave with displacement y=8m sin (2pt/1m x + 4 pt/1s t) what is the wavespeed in meters/second? For the transverse wave with displacement y=8m sin(2 pi/1 m x + 4 pi/1s t) what is the magnitude of the largest transverse velocity in meters/second? For the transverse wave with displacement y = 8m sin(2 pi/1 m x + 4 pi/1s t what is the magnitude of the displacement at x=0.5m and time t=0.5s in meters? For the transverse wave with displacement y=8m sin(2 pi/1m x + 4 pi/1 s t with tension 2N, what is the linear mass density, mu, in kilograms/meter? Two waves of amplitude 1m that are equal in every way have a phase difference (relative phase) of pi/3 radians, what is the amplitude of the superposition of the two waves in meters? A string has two ends 2 meters apart that are fixed, it's tension is 5 Newtons, it's mass density is 3grams/meter what is the frequency (in Hertz) that corresponds to the largest wavelength?

Explanation / Answer

5. assume two waves to be y1 = Asin(wt - kx), y2 = Asin(wt - kx + pi/3)
y1 + y2 = A(sin(wt - kx) + sin(wt - kx + pi/3)) = A(2sin((wt - kx + wt - kx + pi/3)/2)cos((wt - kx - wt + kx - pi/3)/2)) = 2Acos(pi/6)sin(wt - kx + pi/6)
Amplitude = 2Acos(pi/6) = 1.732A
6. l = 2m
T = 5N
mu = 0.003 kg/m
v = sqroot(T/mu ) = 40.824 m/s
largest wavelength, lambda = l*2 = 4m
v = lambda*f
f = 40.824/4 = 10.206 Hz

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