Question

From the given relation y= sin ( wt - kx ). Find out the dimension formula of a , w , and k

please answer it correctly ​

Answer 1

y= A sin ( wt - kx )

dimensional formula of A, w and k

wt - kx are in subtraction than w and k has same dimensional formula

wt - kx has no dimension ( dimensionless )

No dimension = [ M^0 L^0 T^0 ] = 1

for w

wt = 1

w = 1/ t

w = 1/[T]

w = [ T^-1 ] ( T inverse )

for k

kx = 1

k = 1/x

k = 1/ [ L ]

k = [ L^-1] ( L inverse )

( wt - kx ) is dimension less because it is theta and theta has no dimension ( dimension less )

as explain below

y = sin ( theta )

y = perpendicular / hypotenuse

y = [ L ] / [ L ]

y = 1

for A

A is amplitude

y= A sin ( wt - kx )

• sin(wt - kx) = 1

y = A × 1

A = y

A = [ L ]