Question

Doubt, please help

Answer 1

Sure, post it.

Answer 2

its a physics based math problem

Answer 3

Calculus

Answer 4

This red portion, I didn't understand.

Answer 5

=1/2????

Answer 6

He said about some calculus trick!

Answer 7

@IrishBoy123 Math based Physics problem

Answer 8

so i think the first diagram is of sin(kx-wt) so this has name the sinusoid and the second
is the diagram of sin^2(kx-wt) - in this case the waves are denser by 1/2 because the midle part of first in case of second diagram has eliminated

yes?

this is my opinion

Answer 9

hmmm, @jhonyy9 yes you are right

Answer 10

and then?

Answer 11

i have an easy to follow derivation of this, if you allow me to share.

in one second, the wave travels length \(v\) by definition. all particles in that length \(v\) perform SHM with amplitude \(A\) and angular frequency \(\omega\). now the mass of all these particles is \(\text{mass per unit length}\times \text{length} = \mu v\)

now the energy of a particle in SHM is \(\frac{1}2m \omega^2 A^2 = \frac{1}2\mu v \omega^2 A^2 \)and we're done!

Answer 12

yes @ParthKohli but she or he have said that dont understand the red part

Answer 13

Its he :D

Answer 14

that's probably the "average" value of the whole function over one wavelength

Answer 15

yes

http://www.wolframalpha.com/input/?i=integrate+sin%5E2+x+from+0+to++2pi

Answer 16

yes @ParthKohli is absolutely right.
But I needed the solution of the mathematical part

Answer 17

I mean the red part, why 1/2 using calculus

Answer 18

or Lewin here from about 40 mins onwards:
https://www.youtube.com/watch?v=Tul2JfUEnpA

he's prob as good as it gets.

Answer 19

\[\frac{1}{\lambda} \int_{0}^{\lambda} \sin^2 \left(\frac{2\pi}{\lambda} x\right)dx = \frac{1}2 \]

Answer 20

Ok I appreciate the help @IrishBoy123 and @ParthKohli . I will look into the video and see and post it back here....
Thanks a lot

Answer 21

@ParthKohli , why did you do the last step?

Answer 22

@ganeshie8

Answer 23

@Astrophysics

Answer 24

@AravindG

Answer 25

@Abmon98

Answer 26

if we use calculus,
then its x/2+some cosine function

Answer 27

what happened to the x and also cosine function?