Question

In the equation, y = A sin( wt - kx ), obtain the dimensional formula ' w ' and ' k '. Given ' x ' is distance and ' t ' is time.

Answer 1

y = A sin(wt - kx)

For the terms to be subtracted they should have same units/dimensional formula.
wt = kx = rad

From above
wt = rad
w = rad / s

Also,
kx = rad
k = rad/m

Dimension formula of
w = [T^-1]
k = [L^-1]

Answer 2

Answer:

w = $T^{-1}$ ;

k = $L^{-1}$

Explanation:

y = A sin ( wt - kx )

where,

t = time,                       (GIVEN)

x = distance                (GIVEN)

Now,

y = A sin theta

theta = ( wt - kx )

Therefore, ( wt - kx ) is dimensionless.

WT = M^0 L^0 T^0

W = M^0 L^0 T^-1

kx = M^0 L^0 T^0

k = M^0 L^-1 T^0

Hence,

w = $T^{-1}$ ;

k = $L^{-1}$

Hope you found that Helpful !