AOA
2009 question about waves

Describe waves and its types. Derive an expression for speed of waves on a streched string by newton 2nd law

ANS
Waves
"wave is a disturbance that propagates through space and
time, usually with the transference of energy.”


All the waves have some special features and they fulfill these criteria…
Reflection……wave’s direction changes after hitting a reflective surface
Refraction……wave direction changes due to change in speed while entering in anew medium
Diffraction……wave’s when interact with obstacles in their path they are bend
Dispersion…….they can split up by their frequency
Rectilinear motion…..they always follow the straight path

Types of waves

there are three types of waves as under


Mechanical waves require a material medium to travel (air, water, ropes). These waves are divided into three different types.
Transverse waves cause the medium to move perpendicular to the direction of the wave.
Longitudinal waves cause the medium to move parallel to the direction of the wave.
Surface waves are both transverse waves and longitudinal waves mixed in one medium.
Electromagnetic waves do not require a medium to travel (light, radio).
Matter waves are produced by electrons and particles.

By moving a rope once, a single vibration is produced. This is a pulse.
waves can also be divid on the basis of dimension so there are three type of wave
1 dimensional e.g waves move along string or spring
2 dimensional e.g water waves
3 dimensional e.g sound waves

plz senior check is this material enough for this ans

regards

where is the ans for
Derive an expression for speed of waves on a streched string by newton 2nd law

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@ravila
this is mathematical derivation i dont have any software to write mathematical derivation so i am unable to upload its ans
regards

hmmm,.ok

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@ravila
if it is possible for you, please you upload it
regards

right now i have not even touch a single topc from mechanics portion.asking it from you to get an idea ,how to prepare it!
but after getting its material i will definatly share it

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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)

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any one from seniors or other members ,what is Gradient? could anyone help me in explaining it...

@ mahwish
zindagi rahi tu insALLAH tomorow i must do.........
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@ very special1
I am waiting