A transverse wave on a string has amplitude 0.300 cm, wavelength 12.0 cm, and sp

Question

A transverse wave on a string has amplitude 0.300 cm, wavelength 12.0 cm, and speed 6.00 cm/s. It is represented by equation y(x,t) = A cos [ (2pi/ wavelength ) (x - vt) ] At time t = 0, compute y at 1.5 cm intervals of x (that is, at x = 0, x = 1.5 cm, x = 3.0cm, and so on) from x = 0 to x = 12.0 cm. Graph the results. This is the shape of the string at time t = 0. Repeat the calculations for the same values of x at time t = 0.400 s. Graph the shape of the string at these instants. Repeat the calculations for the same values of x at time t = 0.800 s. Graph the shape of the string at these instants. NEED WHAT THE GRAPH LOOKS LIKE BETWEEN 0-12!

Explanation / Answer

x = 0,

y(x,t) = A cos((2/)(x - vt))

y = 0.3 * cos(2*3.1416/12 * (0))

y = 0.3 cm

-----------------------------------------------------

x = 1.5 cm,

y(x,t) = A cos((2/)(x - vt))

y = 0.3 * cos(2*3.1416/12 * (1.5))

y = 0.212 cm

-----------------------------------------------------

x = 3.0cm

x = 1.5 cm,

y(x,t) = A cos((2/)(x - vt))

y = 0.3 * cos(2*3.1416/12 * (3))

y = 0.0 cm

-----------------------------------------------------

x = 4.5cm

x = 1.5 cm,

y(x,t) = A cos((2/)(x - vt))

y = 0.3 * cos(2*3.1416/12 * (4.5))

y = -0.212 cm

-----------------------------------------------------

x = 6cm

x = 1.5 cm,

y(x,t) = A cos((2/)(x - vt))

y = 0.3 * cos(2*3.1416/12 * (6))

y = -0.3 cm

-----------------------------------------------------

x = 7.5cm

x = 1.5 cm,

y(x,t) = A cos((2/)(x - vt))

y = 0.3 * cos(2*3.1416/12 * (7.5))

y = -0.212 cm

-----------------------------------------------------

x = 9 cm

x = 1.5 cm,

y(x,t) = A cos((2/)(x - vt))

y = 0.3 * cos(2*3.1416/12 * (9))

y = 0 cm

-----------------------------------------------------

x = 10.5 cm

x = 1.5 cm,

y(x,t) = A cos((2/)(x - vt))

y = 0.3 * cos(2*3.1416/12 * (10.5))

y = 0.212 cm

-----------------------------------------------------

x = 12 cm

x = 1.5 cm,

y(x,t) = A cos((2/)(x - vt))

y = 0.3 * cos(2*3.1416/12 * (12))

y = 0.3 cm

-----------------------------------------------------

-----------------------------------------------------------------------------

AT t = 0.400 s

y(x,t) = A cos((2/)(x - vt))

y = 0.3 * cos(2*3.1416/12 * (x-6*0.400))

---------------------------------------------------------------------------------

AT t = 0.800 s

y(x,t) = A cos((2/)(x - vt))

y = 0.3 * cos(2*3.1416/12 * (x-6*0.8))

x y 0 0.092704 1.5 0.267302 3 0.285317 4.5 0.136196 6 -0.09271 7.5 -0.2673 9 -0.28532 10.5 -0.13619 12 0.092708

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