Stationary waves

@qwerty

I did not understand you completely.
Can you find the direction of any one wave by using that method so that it will be more clear?

yup i m sorry swordy i misguided u in beginning actually i did not read waves till then properly now i m pretty sure they will form![1]

Thanks!!
That helped.

wave shape isnt changing with time .
what you are talking is about ∂f/∂t , i.e assuming x =constant, i.e you are talking for a particular x . If you fix x, then f represents diplacement of the element at x as a function of time .

hmm....dx/dt is coming to be opposite in sign in two cases. So my book is wrong right?

yes you can find the direction .

@talwarmachhli
just now ur friend jeemacchi came and told me that book is correct!

if f(x,t) is the wave shape , then assuming that it doesnt change, df/dt =df/dx = 0

from either of the two you will get v = dx/dt or v=-dx/dt . That way you can decide the direction

it clearly represents the standing wave for any wave torepresent a standing wave there shoyld exist fixed points at a given time t at different cordinates this is clearly possible if you sole the cos term.

You mean there shouldn't be any constant (eg. Î /4) too ?

combining the 2 eqs ,i m getting y=2Asin(π/4 +ωt)cos(kx-π/4) ;

To represent a standing wave the eq must be of the form ....
y=2Asin(ωt)cos(kx)

so it will not form a stationary wave

Swordifsh,the waves are of same amplitude,frequency and they are moving in the opposite directions.You can visualise that when they will collide then what will happen.

which way then? be more clear.

its not that way swordy!

we can write first wave as y=Asin(90-wt+kx)
Now is the direction of a wave decided by the sign of wt or kx ?