# (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 *D**y* = 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 ****+***y ***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*)=*a*sin(*b**x*+*ϕ*1)cos(*q**t*+*ϕ*2)

D) Calculate a

E) Calculate b

F) Calculate *q*

G) Calculate the smallest possible positive value of *ϕ*1

H) Calculate the smallest possible positive value of *ϕ*2

## 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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