Simple standing waves problem

  • Thread starter nil1996
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  • #1
nil1996
301
7

Homework Statement


Hello everyone,
I am stuck with a basic concept.How do we can recognize if a given equation is wave or not?For example we know that the standing waves equation is y=2Acos(kx)sin(ωt). In my text book there is a problem which says that two waves having only different amplitudes are traveling on opposite directions on x-axis. They have asked if the waves form standing waves.


Homework Equations





The Attempt at a Solution


First of all i wrote the following equations.
y1=A1sin(kx-ωt) ; y1=A2sin(kx+ωt)
i added them and got
y1+y2= (A2+A1)sin(kx)cos(ωt)+(A2-A1)coskxsinωt

how do i recognize if this equation represents a standing wave or not??
 

Answers and Replies

  • #2
NihalSh
199
15
The standing waves have pretty neat definition.

Standing wave is formed when two waves of the same amplitude and frequency, travelling with the same speed in opposite directions interfere (add up).

I guess, this gives you the answer!!!

For a given function ##h## to be a travelling wave, it must be of the form ##h(x-vt)##, where v is velocity of wave.
 
  • #3
nil1996
301
7
The standing waves have pretty neat definition.



I guess, this gives you the answer!!!

For a given function ##h## to be a travelling wave, it must be of the form ##h(x-vt)##, where v is velocity of wave.

i was thinking the same but my book says that it forms standing waves and also transports energy
 
  • #4
NihalSh
199
15
i was thinking the same but my book says that it forms standing waves and also transports energy

standing waves in general form pattern in which point of minimum and maximum displacement don't change with time, moreover in general there is no transport of energy over large distance.

Maybe author of your book wants to make a point!!!

You can check this out at: http://www.physics.buffalo.edu/claw/Page15/ProjectCLAW-P15.html [Broken]

Edit: The equation you found can be considered to be superposition of two standing waves. But it won't reproduce pattern characteristic of standing waves!!!!
 
Last edited by a moderator:
  • #6
NihalSh
199
15
Last edited:
  • #7
nil1996
301
7
a wave cannot be both travelling as well as standing because both are complementary to each other!!!

I meant to say partially traveling.
thanks for guidance:smile:
 
  • #8
NihalSh
199
15
I meant to say partially traveling.
thanks for guidance:smile:

no problem!!!:wink:
 

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