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

Question

For the transverse wave with displacement y = 8 m sin (2pi/1m x+ 4 pi/1s t)what is the wavespeed in meters/second? For the transverse wave with displacement y=8m sin(2pi/1m 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 (2pi/1m 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=8 m sin (2pi/1m x+ 4 pi/1s t) with tension 2N, what is the linear mass density, mu, in kilograms/meter? 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? 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

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 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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