Question

show that v=fλ is dimensionally correct​

Answer 1

To show:

v=fλ is dimensionally correct

Solution:

• For dimensional analysis, we will try to match the LHS AND RHS portion of the equation.

LHS:

$\rm \therefore \: [v] = [L{T}^{ - 1} ]$

Now, RHS :

$\therefore \: [f \times \lambda]$

$= \: [{T}^{ - 1} \times L ]$

$= \: [L{T}^{ - 1} ]$

So, LHS = RHS , hence equation is dimensionally correct.

Answer 2

Answer:

V= fλ

L/T= 1/T × L

L/T= L/T

Explanation:

In this equation on L.H.S V is the velocity , its formula is Displacement upon time , Displacement dimension is L ,time dimension is T so velocity dimensiom becomes L/T . On R.H.S f is frequency and its the reciprocal of timeperiod so its dimension becomes 1/T and λ is wavelength so its dimension is L so 1/T×L becomes L/T and the L.H.S become equal to R.HS