Calculating Water Wave Angle at Different Positions | Wave Length Question

[mustang1988]

1. Water waves having parallel crests 2.0 cm apart pass through two openings 5.2 cm apart in a board. At a point 2.0 m beyond the board, at what angle relative to the "straight-through" direction would there be little or no wave action?
a)closest position to the "straight through" line
b)next closest position from the "straight through" line


2. x=L$$\theta1$$=L($$\lambda$$/d)



3. I was just wondering where to get the wave length from? Would it be 2 since it is 2cm from crest to crest? thanks

 

[anathema]

I would like to address your questions regarding water waves passing through two openings in a board and the concept of wavelength.

Firstly, to answer your first question, at a point 2.0 m beyond the board, the angle relative to the "straight-through" direction where there would be little or no wave action would depend on the wavelength of the water waves. This can be calculated using the formula x = Lθ, where x is the distance from the center of the board to the point where the wave action is minimal, L is the distance between the two openings in the board (5.2 cm in this case), and θ is the angle relative to the "straight-through" direction. To find the angle, we can rearrange the equation to θ = x/L. Therefore, the angle would be minimal when x is equal to L, which in this case would be 5.2 cm.

Next, your second question is regarding the concept of wavelength. Wavelength is the distance between two consecutive crests or troughs of a wave. In this scenario, the wavelength of the water waves passing through the two openings in the board would be equal to the distance between two consecutive crests, which is 2.0 cm. This is because the water waves have parallel crests that are 2.0 cm apart.

I hope this clarifies your doubts. If you have any further questions, please feel free to ask. I am always happy to help and discuss scientific concepts.

 

[kerimek]

First of all, let me clarify that the term "water wave angle" is not commonly used in the scientific community. The correct term for what you are describing is the angle of incidence, which is the angle at which the wave approaches the barrier.

Now, to answer your question, the angle of incidence can be calculated using the formula x=Lθ, where x is the distance between the two openings, L is the distance between the barrier and the point where you want to measure the angle, and θ is the angle of incidence. The value of θ will depend on the wavelength (λ) and the distance between the openings (d).

In this case, since the wavelength is not given, we can use the formula λ=dθ to determine the wavelength. The value of θ will vary depending on the distance from the barrier. At the closest position to the "straight-through" line, the angle of incidence will be 0 degrees, meaning there will be no wave action. As you move away from this point, the angle of incidence will increase, resulting in more wave action.

To answer your second question, the wavelength (λ) is not equal to the distance between crests (2 cm in this case). The wavelength is the distance between two successive crests or troughs. So, in this case, the wavelength will be 4 cm (2 cm from crest to trough + 2 cm from trough to next crest).

I hope this helps clarify your understanding of water waves and their angles of incidence at different positions. Keep exploring and learning about this fascinating topic!