Question

The function y(x,t) = 0.3 sin( 2 π t -2 π x + π /4) represents the vertical position of an element of a taut string upon which a transverse wave travels. This function depends on the horizontal position along the string, x, and time, t. y and x are in units of meters and t is in units of seconds. Do not use symbols in any of your answers below. Only use integers or decimals.

a. Determine the angular frequency. ω =........ rad/s

b. Determine the frequency. f =........ Hz

c. Determine the wave number. k = ........... 1/m or m^-1

d. Determine the direction of travel of the wave. Select an answer (positive x-direction or negative x-direction )

e. Determine the wavelength of the wave. λ = ........ m

f. Determine the speed of the wave. ν = .......... m/s

g. Calculate the maximum transverse speed of an element of the string.
v_y =......... m/s

h. Calculate the maximum transverse acceleration of an element of the string.
a_y =.......... m/s

i. Determine the vertical position of an element of the sting when t = 0.18 s and x = 2.1 m. y =........ m

j. Determine the transverse speed at t = 0.18 s for an element of the string located at x = 2.1 m. v_y = ......... m/s

k. Determine the transverse acceleration at t = 0.18 s for an element of the string located at x = 2.1 m. v_y = ......... m/s²

Answer 1