Answer to Question #163866 in Other for James Woatsi

Question #163866

Show that ¥(x,t)= Asin(wt+kx) describes a wave motion


1
Expert's answer
2021-02-16T12:14:42-0500

Answer:


Step 1

Given:

ψ(x,t)=Asin(wt+kx)


Step 2

Calculation:

ψ(x,t)=Asin(wt+kx)

ψx,t=Asinwt+kx


We know the wave equation is


= →(1)


let us find out all the derivatives 


=Ak cos(wt+kx)


Again differentiate with respect to x,


= Ak2  sin(wt+kx)(Sinceψ(x,t)=Asin(wt+kx)


=−k2ψ(x,t)→(2)


Step 3

Now,Let's find out time derivatives 


=Aw cos(wt+kx)


Again differentiate with respect to x,



=−Aw2 sin(wt+kx) (Sinceψ(x,t)=Asin(wt+kx)



= −wψ(x,t)→(3)


Put the values in(1) equation (2) & (3)


−k2 ψ(x,t)= −w2 ψ(x,t)


Step 4

v2 ψ(x,t)= ψ(x,t)

(Since one dimensional wave equationv= and v2 = )



v2 ψ(x,t)=v2 ψ(x,t)


Hence it is proved.



Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

Ask Your question

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS