For the transverse wave with displacement y=8mm sin ((2 pi x/1m) +(4 pi t/1s)) w

Question

For the transverse wave with displacement y=8mm sin ((2 pi x/1m) +(4 pi t/1s)) what is the wave speed in meters/second? (Answer with a pure number, in decimal form, with three significant figures, such as 1230 or 1.23 or 0.0123) For the transverse wave with displacement y=8mm sin ((2 pi x/1m) + (4 pi t/Is)) what is the magnitude of the *largest* transverse velocity in meters/second? (Answer with a pure number, in decimal form, with three significant figures, such as 1230 or 1.23 or 0.0123) For the transverse wave with displacement y=8mm sin ((2 pi x/1m) + (4 pi t/1s)) what is the magnitude of the displacement at x=0.5m and time t=0.5s in meters? (Answer with a pure number, in decimal form, with three significant figures, such as 1230 or 1.23 or 0.0123) For the transverse wave with displacement y=8mm sin ((2 pi x/lm)+(4 pi t/1s)) with tension 2N, what is the linear mass density mu in kilograms/meter? (Answer with a pure number, in decimal form, with three significant figures, such as 1230 or 1.23 or 0.0123) Two waves of amplitude lm 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? (Answer with a pure number, in decimal form, with three significant figures, such as 1230 or 1.23 or 0.0123)

Explanation / Answer

1)
y = 8*sin (2pi x + 4pi*t)
compare it with,
y = A* sin (kx + wt)

k = 2*pi
use,
k = 2*pi/lambda
lambda = 1 m

w = 4*pi
use:
w = 2*pi*f
f = 2 Hz

wave speed,
v = f*lambda
= 2* 1
= 2 m/s

2)
y = 8*sin (2pi x + 4pi*t)
v = dy/dt = 8*4*pi*cos (2pi x + 4pi*t)
vmax = 8*4*pi
= 32*pi
=100.5 mm/s
= 0.1005 m/s
3)
y = 8*sin (2pi x + 4pi*t)
put x=0.5 and t=0.5
y = 8*sin (2pi *0.5 + 4pi*0.5)
= 8*sin (pi + 2pi)
= 8*sin (3pi)
= 8*0
= 0 m

I am allowed to answer only 1 question at a time but I have answered 3

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