Question

The equation of stationary wave is y = 2A sin kx coswt ( in meter) . Where A and x are in meter. w is angular frequency. Dimensions of A/k are_____


A. M^0 L^0 T^0
B. M^0 L^-2 T^0
C. M^0 L^-1 T^1
D. M^0 L ^2 T ^0


Pls explain and answer ( I want the explanation/ steps)

Answer 1

A/k= amplitude / wave no. = m*lemda/2 pie = m*c/ frequency * 2 pic= m(m per sec) /per sec= m^2... my according bro..

Answer 2

Answer:

Option (D) $[M^0L^2T^0]$

Explanation:

A is amplitude, the unit of amplitue is same as that of length

Therefore, the dimensions of amplitude = [L]

x is also distance which is measured in metres. Therefore the dimension of x is [L]

But kx should be a dimensionless quantity because anything whose trigonometric ratio is being calculated should be a dimensionless quantity

Therefore, the dimension of k = $[L^{-1}]$

Now dimension of A/k

$=\frac{\text{Dimension of A}}{\text{Dimension of k}}$

$=\frac{[L]}{[L^{-1}]}$

$=[L^{1+1}]$

$=[L^2]$

$=[M^0L^2T^0]$

Thus Option (D) is the right option.

Hope the answer is helpful.