(Solved) You have a trough 3.60 m long. It is filled with water, and you want to create a standing wave such that a node occurs every 0.30 m

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You have a trough 3.60 m long. It is filled with water, and you want to create a standing wave such that a node occurs every 0.30 m.
A) What is the wavelength of this wave?
B) A leaf floating on the water 0.60 m from the one end of the trough is displaced a vertical distance Dy = 19 mm at t = 3.2 s and the leaf’s displacement has a period of 0.60 s. What is the resultant displacement of the standing wave? Express your answer with the appropriate units. Enter a positive value if the displacement is in the +direction and negative value if the displacement is in the y direction.
C) The correct time-dependent wave function for the standing wave is f(x,t)=asin(bx+ϕ1)cos(qt+ϕ2)
D) Calculate a
E) Calculate b
F) Calculate q
G) Calculate the smallest possible positive value of ϕ1
H) Calculate the smallest possible positive value of ϕ2

Expert Answer


Answer to You have a trough 3.60 m long. It is filled with water, and you want to create a standing wave such that a node occurs every 0.30 m….

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