Question

give the dimensional formula of k for e^kx where x=distance?​

Answer 1

Answer:

In the given equation y=Asin(ωt−kx)

Since, trigonometric function is a dimensionless quantity. So, (ωt−kx)is also dimensionless quantity.

So,

(ωt−kx)=1

ωt=1

[ω]=  

[T]

1

​

=[T]  

−1

 

kx=1

[k]=  

[L]

1

​

=[L]  

−1

Explanation:

Answer 2

Here, e is constant

And equation will be like this : y = A sin ( wt -kx)

( w = omega)

t = Time

x = distance.

y = A sin (wt - Kx). ( trigonometric function is dimensionless )

so, ( wt - Kx ) is also dimensionless.

(wt - Kx) = 1

wt = 1

w = 1 / T

w = ( T) ¹-

( T minus 1 )

Kx = 1

k = 1 / L

K = ( L ) ¹-

( k = L minus 1 )