Find the Optimum Spot to Minimize Wave Action in Large Water Tank Experiment

[simplicity12]

Homework Statement

In a large water tank experiment, water waves are generated with straight, parallel wave fronts, 3.00 m apart. The wave fronts pass through two openings 5.00 m apart in a long board. The end of the tank is 3.00 m beyond the board. Where would you stand, relative to the perpendicular bisector of the line between the openings, if you want to receive little or no wave action?

2. Homework Equations

[P(n)*S(1)] - [P(n)*S(2)] = (n - 1/2)*wavelength

sin ANGLE(n) = (n - 1/2)*wavelength/(distance between sources)

x(n) / L = (n - 1/2) * wavelength / (distance between sources)

The Attempt at a Solution

I tried using the third formula, allowing the n be 1, the wavelength 3.00 m and the distance between the two sources 5.00 m, but i don't know what value i should assign x(n) and L. I don't know if I'm doing the question right. Can anyone help?

 

[Mentz114]

This sounds like 2 slit interference. The points of no wave motion would be the places where the distances from the slits differ by 1/2 wavelength..

 

[m2003]

I would approach this problem by first understanding the physical principles at play. In this experiment, we are dealing with water waves and their interference patterns. The goal is to find the optimum spot where the waves cancel each other out, resulting in little or no wave action.

To determine this spot, we can use the principle of superposition, which states that when two waves meet, the resulting displacement is the sum of the displacements of the individual waves. This means that when two waves meet in opposite phases (crest meets trough), they cancel each other out.

In this case, the two openings in the board act as two coherent sources of waves, with a wavelength of 3.00 m. The perpendicular bisector of the line between the two openings will be the line where the waves from both sources meet in opposite phases. This means that standing on this line will result in little or no wave action.

To determine where this line is, we can use the equation x(n) / L = (n - 1/2) * wavelength / (distance between sources), where x(n) is the position of the line, L is the distance between the two sources (5.00 m in this case), and n is the order of the interference pattern. For the first order (n=1), we get x(1) / 5.00 m = (1 - 1/2) * 3.00 m / 5.00 m, which simplifies to x(1) = 0.3 m. This means that the perpendicular bisector is 0.3 m away from the line connecting the two sources.

Therefore, to minimize wave action, I would stand 0.3 m away from the line connecting the two sources, on the side that is closer to the end of the tank. This is the optimum spot where the waves from the two sources will cancel each other out, resulting in little or no wave action.