Suppose you have a traveling wave on a string that is described by the following

Question

Suppose you have a traveling wave on a string that is described by the following expression (x is in meters and t in seconds):

a. What is the wavenumber? _______
b. What is its angular frequency? ______________
c. What direction is this wave is moving? ________
d. What is the frequency? ________
e. What is the period? ________
f. What is the speed of this wave? __________
g. What is its wavelength? _________
h. What is the height of the wave at x=0 and t=0?
i. Derive an expression for the vertical velocity of a point on the string.

Just need to check my answers fo a-h but I really need help with i.

Explanation / Answer

y(x,t)=(15cm)sin(20.0x+0.5t-pi /3.0)

compare with standard equation

Y = A sin (kx + wt - phi)

a. wavenumber , K = 20 m-1

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b.
angular freq , w = 0.5 s-1

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c.
along negative x-axis
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d)

freq , f = w/2pi = 0.5/2pi = 0.0796 Hz

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e)
period T = 1/f = 12.56 sec

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f)

speed , v = w/k = 0.5/20 = 0.025 m/s

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g)

wavelenght L = 2pi/K = 2pi/20 = 0.314 m

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h)

at t = 0 , x = 0

height y = - 13 cm

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i.

V = dy/dt = (7.5 cm/s) cos(20x + 0.5 t - pi/3)

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