Wave interference equations help

[JLPhysics]

Homework Statement

Does anyone know the equations for these? Or a website that could help? I lost my notes about them and I can't find anything on the internet. I have a worksheet of 15 problems and I only have these three left!

A string is attatched to a post at one end. Several pulses of amplitude .15 m sent down the are refelcted back at the post and travel back down the string without loss of amplitude. What is the amplitude at a point on a string where the maximum displacement points of two pulses cross? What type of interferance is this? How would your answer change if the same pulses were sent down a string whose end is free? What type of interfrence is this?

--------------------------------------------------------------------------------------
A streched string fixed at both ends is 2.0 m long. What are three wavelengths that will produce standing waves on this string. Name at least one wavelength that would not produce a standing wave pattern.

Homework Equations

That's what I need to know!

The Attempt at a Solution

I've made a few attempts and it has become clear to me (almost one and a half hours later) that I need help before I continue.

:EDIT: I figured one out on my own!

Any help is greatly welcomed.

 

[temaire]

I know that the website www.physicsclassroom.com has some good notes on waves.

 

[Moetasim]

I would suggest using the wave interference equations to solve these problems. The first problem involves calculating the amplitude at a point where two pulses intersect. This can be done using the superposition principle, which states that the amplitude at any point is the sum of the amplitudes of each individual wave at that point. The equation for this is A = A1 + A2, where A1 and A2 are the amplitudes of the two intersecting pulses.

To determine the type of interference, you can use the equation Afinal = A1 + A2 + 2√(A1A2)cos(Δφ), where Afinal is the final amplitude, A1 and A2 are the amplitudes of the individual waves, and Δφ is the phase difference between them. If Δφ is 0, then the interference is constructive (the amplitudes add up). If Δφ is π, then the interference is destructive (the amplitudes cancel out).

If the same pulses were sent down a string with a free end, the equation for the final amplitude would be Afinal = A1 + A2 + 2√(A1A2)sin(Δφ), where sin(Δφ) represents the phase difference between the two waves. In this case, if Δφ is 0, then the interference is also constructive, but if Δφ is π, then the interference is destructive.

For the second problem, the wavelengths that will produce standing waves on a string fixed at both ends can be calculated using the equation λn = 2L/n, where λn is the wavelength of the nth standing wave, L is the length of the string, and n is the number of nodes (points of zero displacement) in the standing wave. So, for example, if n = 1, then the wavelength would be 2L, and if n = 2, the wavelength would be L.

As for the wavelength that would not produce a standing wave pattern, any wavelength that does not fit the equation for λn would not produce a standing wave. For example, a wavelength of L/2 or 3L/4 would not produce a standing wave on a string fixed at both ends.

I hope this helps you with your homework. Remember to always refer to the equations and principles that you have learned in class, and don't forget to show your work! Good