Question

A sinusoidal traveling wave is described by the wave function

y = 0.1 sin (4.0π x − 8.0π t)

where x and y are in m and t is in s.

a) At time t = 0, the bit of string at position x = 0.125 m has transverse (in the y-direction) velocity:

b) transverse acceleration:

Answer 1

equation of wavefunction

y = A*sin(kx - wt)

given expression

y = 0.1*sin(4pix - 8pit)

speed v = dy/dt

v = -0.1*cos(4pix - 8pit)*8*pi

v = -0.8*pi*cos(4pix - 8pit)

at time t = 0   and x = 0.125 m

v = -0.8*pi*cos((4*pi*0.125)-0)

v= 0 m/s <<<<<=======ANSWER

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b)

acceleration a = dv/dt

a = -0.8*pi*sin(4pix - 8pit)*8pi

a = -6.4*pi^2*sin(4pix-pit)

at time t = 0 , x = 0.125

a = -6.4*pi^2*sin(4*pi*0.125-0)

a = -63.16 m/s <<<<<=======ANSWER