Angle Maxima and nodes and antinodes

[jamieXX96]

Homework Statement

I have attached the problem...

Homework Equations

dsin([itex]\theta[/itex]) = [itex]\lambda[/itex]m

The Attempt at a Solution

(0.00003m)(sin([itex]\theta[/itex])) = (0.000000550m)(2) ------------> 2.10^o
(0.00003m)(sin([itex]\theta[/itex])) = (0.000000550m)(3) ------------> 3.15^o


I looked through my textbook, but the only piece that I could find about nodes/anti-nodes was the diagram that I attached. Can someone explain how I draw them/what they are?

THANKS SO MUCH!

 

[tiny-tim]

welcome to pf!

hi jamieXX96! welcome to pf!

replace those red wavy lines by red straight lines …

the https://www.physicsforums.com/library.php?do=view_item&itemid=190" path difference is the difference in the lengths of the two lines

 

[jamieXX96]

Thanks!
But how would I show how the nodes and anti-nodes are created?

 

[tiny-tim]

for wavelength λ, it's an anti-node if the path difference is … ?

 

[rwisz]

I can explain the concept of angle maxima, nodes, and antinodes in relation to the problem you have attached.

Angle maxima refers to the maximum angle at which a wave is observed. In this case, it is the maximum angle at which the wave is reflected off the surface. This angle can be calculated using the equation dsin(\theta) = \lambda, where d is the distance between the two reflecting surfaces, \theta is the angle of incidence, and \lambda is the wavelength of the wave.

Nodes and antinodes refer to the points along the wave where the amplitude is either zero (nodes) or maximum (antinodes). In the attached diagram, the red dots represent the nodes, while the blue dots represent the antinodes. The distance between two consecutive nodes or antinodes is equal to half the wavelength of the wave.

To draw nodes and antinodes, you can use the equation for the standing wave pattern, y(x) = A sin(kx)cos(\omega t), where A is the amplitude, k is the wave number, x is the position along the wave, and \omega is the angular frequency. You can plot this equation for different values of x and t to see how the wave behaves and where the nodes and antinodes are located.

I hope this explanation helps you understand the concept of angle maxima, nodes, and antinodes better. If you have any further questions, please do not hesitate to ask. Happy studying!