(a) Write the expression for y as a function of x and t in SI units for a sinuso
ID: 1790264 • Letter: #
Question
(a) Write the expression for y as a function of x and t in SI units for a sinusoidal wave traveling along a rope in the negative x direction with the following characteristics: A = 7.75 cm, = 85.0 cm, f = 4.00 Hz, and y(0, t) = 0 at t = 0. (Use the following as necessary: x and t.)
(a) Write the expression for y as a function of x and t in SI units for a sinusoidal wave traveling along a rope in the negative x direction with the following characteristics: A 7.75 cm, = 85.0 cm, f= 4.00 Hz, and y(0, t) = 0 at t-0. (Use the following as necessary: x and t.) y= (b) Write the expression for y as a function of x and t for the wave in part (a) assuming y(x, 0)0 at the point x 22.5 cm. (Use the following as necessary: x and t.) 22.5 cm. (Use the following as necessary: x and t.)Explanation / Answer
given
A= 7.75 cm= 0.0775 m
k = 2pi/ lamda = 2pi/0.85 m = 2.35 pi m^-1
w = 2 pi f = 2pi ( 4) = 8 pi rad/s
when th ewave travelling in negative x direction the general equation is
y = A sin ( wt + kx + phi)
consider phi = 0
y = 0.0775 sin ( 2.35 pi x + 8 pi t)
(b)
y( x,0) = 0.0775 sin ( 2.35 pi x + 8 pi t + phi)
substitue x = 0.225 m and t= 0
y( x,0) = 0.0775 sin ( 2.35 pi (0.225) + 8 phi (0)+ phi)
0 = 0.0775 sin ( 0.529 pi + phi)
0 = 0.0775 sin ( 0.529 pi + phi)
then to become LHS = 0 , phi should be = -0.529 pi
y ( x,0) = 0.0755 sin ( 0.529 pi + 8 pi t - 0.529 phi)
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