waves and its types.....past paper question - Page 2

very special 1 · #11 Thursday, September 22, 2011

Quote:

Originally Posted by adventurous

newton's 2nd law;
F=ma, here F=-kx
we ger -kx=ma
write a= (d^2 x/dt^2) that is, in differential form

We get the general equation of wave by puttind the value of acceleration in above equation as;

d2x/dt2 + kx/m = 0
or d2x/dt2= -kx/m (1)
Employing numercal analysis, we can find the possible roots of above eqaution in the form of x;
the tentative form of soln of above equation wud b;
X=Xm Cos(wt+ phi)
differentiate it twice so that we may compare it with the general wave equation as written above;
After diff, we will get

d2x/dt2= -(w^2)Xm Cos(wt + phi) (2)

compare (1) and (2)
w^2= k/m

w= square root (k/m)

@ adventuours
the question is about the speed of the wave not about the angular frequancy...
the expression of wave speed is v = square root F/ u(mue) and mue = delta m/delta l
so derive wave speed plz
regards

adventurous · #12 Thursday, October 06, 2011

sorry for so late reply.. I wasnt visiting forum very often.
So, my bad for going astray;
I dont have the derivation with me now(did prepare physics while i was in village and now moved to city for some academy, so my physics derivation register is at home)
but I will try to make it easier for you;
Step 1:
you can derive a wave eqaution in the form
d2y/dx2= (1/v^2)* dy2/dt2 _________(1)

I feel one may directly write it in exam as its a well known equation or derive it from simple y=Ym*Sin(kx -wt) in two steps;
a- double diff y w.r.t x to get left hand side and double diff y w.r.t. "t"
b- compare both side and put w/k=v; you will get the wave equation.

The second equation is much difficult and lengthy to derive
from newton secong law, get f=ma
using some sine/cosine identities we express the forces in Y direction as related to X directionwith the help of a figure of the string;
you will finally get a form as

d2y/dx2= (u/F) d2y/dt2_________(2)

compare 1 and 2 and get v=squareroot(F/u)

I can upload details when i visit home if someone needs.

For gradient, visit wikipedia page for definition and explanation
in simple terms;
It is an operator that turns a scalar function/field into a vector.(for easy understanding)

theoretically; if we apply this operator on some function, it gives a vector that points towards max slope/change of the function in any direction.
e.g if we apply this operator on a function f(x) which represents temperature in a room,
the resultant will be a vector that points to max. temperature change in the room along any direction(as defined by function/field).

Mathematics;
Its diificult to make mathematics understandable in this writing format, search some examples of it online.

very special 1 · #13 Thursday, October 06, 2011

Quote:

Originally Posted by adventurous

sorry for so late reply.. I wasnt visiting forum very often.
So, my bad for going astray;
I dont have the derivation with me now(did prepare physics while i was in village and now moved to city for some academy, so my physics derivation register is at home)
but I will try to make it easier for you;
Step 1:
you can derive a wave eqaution in the form
d2y/dx2= (1/v^2)* dy2/dt2 _________(1)

I feel one may directly write it in exam as its a well known equation or derive it from simple y=Ym*Sin(kx -wt) in two steps;
a- double diff y w.r.t x to get left hand side and double diff y w.r.t. "t"
b- compare both side and put w/k=v; you will get the wave equation.

The second equation is much difficult and lengthy to derive
from newton secong law, get f=ma
using some sine/cosine identities we express the forces in Y direction as related to X directionwith the help of a figure of the string;
you will finally get a form as

d2y/dx2= (u/F) d2y/dt2_________(2)

compare 1 and 2 and get v=squareroot(F/u)

I can upload details when i visit home if someone needs.

For gradient, visit wikipedia page for definition and explanation
in simple terms;
It is an operator that turns a scalar function/field into a vector.(for easy understanding)

theoretically; if we apply this operator on some function, it gives a vector that points towards max slope/change of the function in any direction.
e.g if we apply this operator on a function f(x) which represents temperature in a room,
the resultant will be a vector that points to max. temperature change in the room along any direction(as defined by function/field).

Mathematics;
Its diificult to make mathematics understandable in this writing format, search some examples of it online.

@ adventurous
i think now this question is complete........
first portion ans how much marks you will give?
yup now derivation is right........i understand it
regards

adventurous · #14 Thursday, October 06, 2011

hmmm....
I can expect above average marks for an answer, but it wud be my first attempt this time , so idea about how marks are awarded here :s

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