Reflection of a mechanical wave

when a mechanical wave is reflected by a fixed support it experiences a phase change of pi .... without getting into maths can i qualitatively prove this ? i cannot analyse how the forces will be acting .
 

rbj

2,221
7
let's assume this is a one-dimensional wave problem (wave on a stretched out string). the diff eq. describing it is likely:

[tex] c^2 \frac{\partial^2 y}{\partial x^2} = \frac{\partial^2 y}{\partial t^2} [/tex]

a general solution is

[tex] y(x,t) = y_1(x-ct) + y_2(x+ct) [/tex]

where c is the wavespeed and [itex] y_1(.), y_2(.) [/itex] can be anything and have to be determined by initial conditions. [itex] y_1(x-ct) [/itex] is a wave moving in the +x direction and [itex] y_2(x+ct) [/itex] is a wave moving in the -x direction and the two waves just add up (superimpose). now let's say that your string is anchored at x=0. that means that

[tex] y(0,t) = y_1(-ct) + y_2(ct) = 0 [/tex]

for all time t. now about the only way for that to happen is if

[tex] y_1(-ct) = -y_2(ct) [/tex]

that means, at x=0, that the wave that is moving in one direction has to be the exact negative of the wave moving in the other direction for them to add to zero and they have to add to zero because of the "fixed support". reversing the polarity is the same as a phase change of [itex] \pi [/itex] radians.
 

Meir Achuz

Science Advisor
Homework Helper
Gold Member
2,169
63
The easiest way to see the pi pahse change is that the incident and reflected wave mus cancel at the fixed wall. This means the reflected wave must be the negative of the incident wave.
 

Related Threads for: Reflection of a mechanical wave

  • Last Post
Replies
2
Views
6K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
13
Views
4K
Replies
4
Views
5K
  • Last Post
Replies
7
Views
2K
Replies
14
Views
541
Replies
10
Views
5K
Top